```
**Explanation of Tags:**
1. **``**: The most important SEO tag. It's concise, includes the core topic (`Natural Frequency`, `Mass-Spring System`, `SDOF`), the exam context (`GATE ME 2017`), and indicates it's a solution (`Solved Question`).
2. **`<meta name="description">`**: A brief summary of the page's content. It's designed to entice clicks from search results. It includes keywords, the specific question number, and the promise of a solution.
3. **`<meta name="keywords">`**: While less impactful for ranking directly by major search engines now, it still provides contextual information and can be useful for niche search engines or internal site search. I've included a comprehensive list.
4. **`<meta name="author">`**: Identifies the creator of the content.
5. **`<link rel="canonical">`**: Tells search engines the preferred version of a URL, preventing duplicate content issues.
6. **Open Graph Tags (`og:` prefix)**: These tags control how your content appears when shared on social media platforms like Facebook, LinkedIn, etc.
* `og:type`: Specifies the type of content (e.g., `article`, `website`).
* `og:url`: The canonical URL of the page.
* `og:title`: The title for the social media share.
* `og:description`: The description for the social media share.
* `og:image`: The URL of an image that will be displayed with the share. I used the image from the question.
* `og:site_name`: The name of your website.
7. **Twitter Card Tags (`twitter:` prefix)**: Similar to Open Graph, these tags optimize content display when shared on Twitter.
* `twitter:card`: Type of Twitter card (`summary_large_image` is good for content with a prominent image).
* `twitter:site`: The Twitter handle of the website/publisher. (Placeholder provided, replace if you have one).
* `twitter:creator`: The Twitter handle of the content creator (omitted as not provided).
* `twitter:title`, `twitter:description`, `twitter:image`: Similar to their Open Graph counterparts.
8. **Schema.org Microdata (`application/ld+json`)**: This JSON-LD structured data helps search engines understand the content's context more deeply, potentially leading to rich snippets in search results (e.g., showing the question and answer directly).
* I've used `QAPage` (Question and Answer Page) schema, marking the question, its text, the options, and the likely correct answer. This is highly relevant for an exam question page.
* I've also included `isPartOf` to link it to a broader category page (like "GATE Mechanical Engineering 2017 Set 2 Questions") and `publisher` information.
<link href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap/5.3.2/css/bootstrap.min.css" rel="stylesheet">
<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.5.1/css/all.min.css" rel="stylesheet">
<link href="https://fonts.googleapis.com/css2?family=Inter:wght@300;400;500;600;700;800&display=swap" rel="stylesheet">
<style>
:root {
--primary: #6366f1;
--primary-dark: #4f46e5;
--primary-light: #e0e7ff;
--success: #10b981;
--error: #ef4444;
--warning: #f59e0b;
--dark: #0f172a;
--dark-light: #1e293b;
--gray: #64748b;
--gray-light: #f1f5f9;
--white: #ffffff;
--shadow: 0 4px 6px -1px rgba(0, 0, 0, 0.25);
--shadow-lg: 0 20px 25px -5px rgba(0, 0, 0, 0.25);
--border-radius: 16px;
--border-radius-sm: 8px;
}
body {
font-family: 'Inter', -apple-system, BlinkMacSystemFont, sans-serif;
min-height: 100vh;
color: var(--dark);
line-height: 1.6;
}
.background-overlay {
position: fixed;
top: 0;
left: 0;
right: 0;
bottom: 0;
background:
radial-gradient(circle at 25% 25%, rgba(99, 102, 241, 0.1) 0%, transparent 50%),
radial-gradient(circle at 75% 75%, rgba(168, 85, 247, 0.1) 0%, transparent 50%);
pointer-events: none;
z-index: -1;
}
.container {
max-width: 1024px;
margin: 0 auto;
padding: 0 20px;
}
.progress-container {
flex: 1;
max-width: 300px;
margin: 0 20px;
}
.progress-bar {
width: 100%;
height: 8px;
background: var(--gray-light);
border-radius: 20px;
overflow: hidden;
margin-bottom: 4px;
}
.progress-fill {
height: 100%;
background: linear-gradient(90deg, var(--primary), var(--primary-dark));
border-radius: 20px;
width: 20%;
transition: width 0.3s ease;
}
.progress-text {
font-size: 12px;
color: var(--gray);
text-align: center;
}
.question-meta {
display: flex;
align-items: center;
gap: 12px;
}
.question-number {
background: linear-gradient(135deg, var(--primary), var(--primary-dark));
color: white;
padding: 8px 16px;
border-radius: 20px;
font-weight: 600;
font-size: 14px;
box-shadow: var(--shadow);
}
.difficulty {
padding: 6px 12px;
border-radius: 12px;
font-size: 12px;
font-weight: 600;
text-transform: uppercase;
letter-spacing: 0.5px;
}
.difficulty.easy { background: linear-gradient(135deg, #dcfce7, #bbf7d0); color: #166534; }
.difficulty.medium { background: linear-gradient(135deg, #fef3c7, #fde68a); color: #d97706; }
.difficulty.hard { background: linear-gradient(135deg, #fecaca, #fca5a5); color: #dc2626; }
/* Main Content */
.main-content {
padding: 32px 0;
}
.content-wrapper {
display: grid;
grid-template-columns: 1fr 8fr 1fr;
gap: 24px;
align-items: start;
}
.left-spacer,
.right-spacer {
/* Empty spacer columns for large screens */
}
.question-card {
background: var(--white);
border-radius: var(--border-radius);
padding: 20px;
margin-bottom: 24px;
box-shadow: var(--shadow-lg);
border: 1px solid rgba(229, 231, 235, 0.2);
grid-column: 2;
}
/* Question Badge with Menu */
.question-badge-container {
display: flex;
align-items: center;
justify-content: space-between;
margin-bottom: 24px;
position: relative;
}
.question-type-badge {
display: inline-flex;
align-items: center;
gap: 8px;
background: var(--primary-light);
color: var(--primary-dark);
padding: 8px 16px;
border-radius: 20px;
font-size: 13px;
font-weight: 600;
flex: 1;
}
.menu-button {
background: none;
border: none;
color: var(--gray);
font-size: 18px;
padding: 8px;
border-radius: 50%;
cursor: pointer;
transition: all 0.2s ease;
display: flex;
align-items: center;
justify-content: center;
width: 36px;
height: 36px;
position: relative;
}
.menu-button:hover {
background: var(--gray-light);
color: var(--dark);
}
.menu-button.active {
background: var(--primary-light);
color: var(--primary-dark);
}
/* Dropdown Menu */
.dropdown-menu {
position: absolute;
top: 100%;
right: 0;
background: var(--white);
border-radius: var(--border-radius-sm);
box-shadow: var(--shadow-lg);
border: 1px solid rgba(229, 231, 235, 0.3);
min-width: 200px;
z-index: 1000;
opacity: 0;
transform: translateY(-10px);
pointer-events: none;
transition: all 0.3s cubic-bezier(0.4, 0, 0.2, 1);
}
.dropdown-menu.show {
opacity: 1;
transform: translateY(0);
pointer-events: auto;
}
.dropdown-item {
display: flex;
align-items: center;
gap: 12px;
padding: 12px 16px;
color: var(--dark);
text-decoration: none;
font-size: 14px;
font-weight: 500;
border: none;
background: none;
width: 100%;
text-align: left;
cursor: pointer;
transition: background-color 0.2s ease;
border-bottom: 1px solid rgba(229, 231, 235, 0.3);
}
.dropdown-item:last-child {
border-bottom: none;
}
.dropdown-item:hover {
background: var(--gray-light);
}
.dropdown-item i {
color: var(--gray);
width: 16px;
text-align: center;
}
.dropdown-item.contributor {
cursor: default;
color: var(--gray);
font-weight: 400;
}
.dropdown-item.contributor:hover {
background: none;
}
.dropdown-item.contributor .contributor-name {
color: var(--primary-dark);
font-weight: 600;
}
.dropdown-item.report:hover {
background: rgba(16, 185, 129, 0.1);
color: var(--success);
}
.dropdown-item.copyright:hover {
background: rgba(239, 68, 68, 0.1);
color: var(--error);
}
/* Overlay for closing dropdown */
.dropdown-overlay {
position: fixed;
top: 0;
left: 0;
right: 0;
bottom: 0;
z-index: 999;
opacity: 0;
pointer-events: none;
transition: opacity 0.2s ease;
}
.dropdown-overlay.show {
opacity: 1;
pointer-events: auto;
}
.question-text {
font-size: 17px;
font-weight: 600;
color: var(--dark);
margin-bottom: 32px;
line-height: 1.4;
}
/* Enhanced MCQ Options */
.mcq-options {
display: grid;
gap: 10px;
margin-bottom: 32px;
}
.option {
background: var(--white);
border: 2px solid rgba(99, 102, 241, 0.1);
border-radius: var(--border-radius);
padding: 10px;
cursor: pointer;
transition: all 0.3s cubic-bezier(0.4, 0, 0.2, 1);
display: flex;
align-items: center;
gap: 16px;
position: relative;
overflow: hidden;
}
.option::before {
content: '';
position: absolute;
top: 0;
left: 0;
width: 4px;
height: 100%;
background: var(--primary);
transform: scaleY(0);
transition: transform 0.3s ease;
}
.option:hover {
transform: translateY(-2px);
box-shadow: var(--shadow-lg);
border-color: var(--primary);
}
.option:hover::before {
transform: scaleY(1);
}
.option.selected {
background: var(--primary-light);
border-color: var(--primary);
transform: translateY(-2px);
box-shadow: var(--shadow-lg);
}
.option.selected::before {
transform: scaleY(1);
}
.option.correct {
background: linear-gradient(135deg, #f0fdf4, #dcfce7) !important;
border-color: var(--success) !important;
animation: correctPulse 0.6s ease;
}
.option.incorrect {
background: linear-gradient(135deg, #fef2f2, #fecaca) !important;
border-color: var(--error) !important;
animation: incorrectShake 0.6s ease;
}
.option-label {
width: 40px;
height: 40px;
border-radius: 50%;
background: var(--gray-light);
display: flex;
align-items: center;
justify-content: center;
font-weight: 700;
color: var(--gray);
flex-shrink: 0;
transition: all 0.3s ease;
box-shadow: 0 2px 4px rgba(0, 0, 0, 0.1);
}
.option.selected .option-label {
background: var(--primary);
color: white;
transform: scale(1.1);
}
.option.correct .option-label {
background: var(--success);
color: white;
}
.option.incorrect .option-label {
background: var(--error);
color: white;
}
.option-text {
flex: 1;
font-size: 14px;
font-weight: 500;
}
/* Action Buttons */
.actions {
display: flex;
gap: 16px;
justify-content: center;
}
.btn {
padding: 14px 28px;
border-radius: var(--border-radius);
border: none;
font-weight: 600;
cursor: pointer;
transition: all 0.3s cubic-bezier(0.4, 0, 0.2, 1);
font-size: 16px;
display: flex;
align-items: center;
gap: 10px;
text-decoration: none;
position: relative;
overflow: hidden;
}
.btn::before {
content: '';
position: absolute;
top: 0;
left: -100%;
width: 100%;
height: 100%;
background: linear-gradient(90deg, transparent, rgba(255, 255, 255, 0.2), transparent);
transition: left 0.5s;
}
.btn:hover::before {
left: 100%;
}
.btn-primary {
background: linear-gradient(135deg, var(--primary), var(--primary-dark));
color: white;
box-shadow: var(--shadow);
}
.btn-primary:hover {
transform: translateY(-2px);
box-shadow: var(--shadow-lg);
}
.btn-secondary {
background: var(--white);
color: var(--gray);
border: 2px solid rgba(100, 116, 139, 0.2);
}
.btn-secondary:hover {
background: var(--gray-light);
transform: translateY(-1px);
}
/* Explanation Card */
.explanation {
background: linear-gradient(135deg, #f0fdf4, #dcfce7);
border: 1px solid #bbf7d0;
border-radius: var(--border-radius);
padding: 0;
margin-top: 0;
max-height: 0;
opacity: 0;
overflow: hidden;
transition: all 0.4s cubic-bezier(0.4, 0, 0.2, 1);
}
.explanation.show {
max-height: 200px;
opacity: 1;
padding: 24px;
margin-top: 24px;
}
.explanation h4 {
color: #166534;
margin-bottom: 12px;
display: flex;
align-items: center;
gap: 10px;
font-size: 18px;
font-weight: 700;
}
.explanation p {
color: #15803d;
line-height: 1.7;
font-size: 15px;
}
/* Similar Questions */
.similar-section {
background: var(--white);
border-radius: var(--border-radius);
padding: 32px;
margin-bottom: 24px;
box-shadow: var(--shadow-lg);
border: 1px solid rgba(229, 231, 235, 0.2);
grid-column: 2;
}
.section-title {
font-size: 20px;
font-weight: 700;
color: var(--dark);
margin-bottom: 24px;
display: flex;
align-items: center;
gap: 12px;
}
.similar-questions-grid {
display: grid;
gap: 16px;
}
.similar-question {
background: var(--white);
border: 1px solid rgba(99, 102, 241, 0.1);
border-radius: var(--border-radius-sm);
padding: 20px;
cursor: pointer;
transition: all 0.3s cubic-bezier(0.4, 0, 0.2, 1);
position: relative;
overflow: hidden;
}
.similar-question::before {
content: '';
position: absolute;
top: 0;
left: 0;
width: 4px;
height: 100%;
background: var(--primary);
transform: scaleY(0);
transition: transform 0.3s ease;
}
.similar-question:hover {
transform: translateY(-2px);
box-shadow: var(--shadow);
border-color: var(--primary);
}
.similar-question:hover::before {
transform: scaleY(1);
}
.similar-question-text {
font-size: 16px;
color: var(--dark);
margin-bottom: 12px;
font-weight: 500;
line-height: 1.5;
}
.similar-question-meta {
display: flex;
justify-content: space-between;
align-items: center;
font-size: 14px;
color: var(--gray);
}
.question-id {
font-weight: 600;
color: var(--primary);
}
/* Tags */
.tags-section {
background: var(--white);
border-radius: var(--border-radius);
padding: 32px;
box-shadow: var(--shadow-lg);
border: 1px solid rgba(229, 231, 235, 0.2);
grid-column: 2;
}
.tags-grid {
display: flex;
flex-wrap: wrap;
gap: 12px;
}
.tag {
background: var(--white);
color: var(--primary-dark);
padding: 10px 18px;
border-radius: 20px;
font-size: 14px;
font-weight: 500;
border: 2px solid var(--primary-light);
cursor: pointer;
transition: all 0.3s ease;
position: relative;
overflow: hidden;
}
.tag::before {
content: '';
position: absolute;
top: 0;
left: -100%;
width: 100%;
height: 100%;
background: linear-gradient(90deg, transparent, rgba(99, 102, 241, 0.1), transparent);
transition: left 0.5s;
}
.tag:hover::before {
left: 100%;
}
.tag:hover {
background: var(--primary);
color: white;
transform: translateY(-2px);
box-shadow: var(--shadow);
}
/* Animations */
@keyframes correctPulse {
0%, 100% { transform: scale(1); }
50% { transform: scale(1.02); }
}
@keyframes incorrectShake {
0%, 100% { transform: translateX(0); }
25% { transform: translateX(-4px); }
75% { transform: translateX(4px); }
}
/* Responsive Design */
@media (max-width: 768px) {
.container {
padding: 0 16px;
}
.content-wrapper {
grid-template-columns: 1fr;
gap: 16px;
}
.question-card,
.similar-section,
.tags-section {
grid-column: 1;
padding: 24px 20px;
}
.header-content {
flex-wrap: wrap;
}
.progress-container {
order: 3;
flex-basis: 100%;
max-width: none;
margin: 12px 0 0 0;
}
.question-text {
font-size: 17px;
}
.option {
padding: 16px;
gap: 12px;
}
.option-label {
width: 36px;
height: 36px;
}
.actions {
flex-direction: column;
}
.btn {
width: 100%;
justify-content: center;
}
.section-title {
font-size: 18px;
}
.main-content {
padding: 24px 0;
}
.dropdown-menu {
right: -10px;
min-width: 180px;
}
}
@media (max-width: 480px) {
.logo {
font-size: 20px;
}
.question-number {
padding: 6px 12px;
font-size: 12px;
}
.question-text {
font-size: 18px;
}
.option {
padding: 14px;
gap: 10px;
}
.option-label {
width: 32px;
height: 32px;
font-size: 14px;
}
.btn {
padding: 12px 20px;
font-size: 15px;
}
.content-wrapper {
grid-template-columns: 1fr;
gap: 12px;
}
.question-card,
.similar-section,
.tags-section {
grid-column: 1;
padding: 20px 16px;
}
}
/* Loading state */
.loading {
display: inline-block;
width: 20px;
height: 20px;
border: 3px solid rgba(255, 255, 255, 0.3);
border-radius: 50%;
border-top-color: #fff;
animation: spin 1s ease-in-out infinite;
}
@keyframes spin {
to { transform: rotate(360deg); }
}
</style>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
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<div class="notification-dropdown">
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<button class="profile-btn" id="profileBtn">
<i class="fas fa-user"></i>
</button>
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Mechanical Engineering > GATE 2017 SET-2 > Natural Frequency
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A mass m is attached to two identical springs having spring constant k as shown in the figure. The natural frequency ω of this single degree of freedom system is
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window.closeLoginModal();
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if (loginModal) {
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e.stopPropagation();
});
}
}
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function markAsRead(notificationId) {
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notification.unread = true;
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notificationBadge.textContent = unreadCount;
notificationBadge.style.display = unreadCount > 0 ? 'block' : 'none';
}
if (notificationMenu) {
notificationMenu.innerHTML = generateNotificationContent();
}
});
}
}
// Initialize when DOM is loaded
document.addEventListener('DOMContentLoaded', function() {
console.log('DOM loaded, initializing...');
initializeNotifications();
initializeProfile();
initializeLoginModal();
});
// Function to add new notification (for testing or real-time updates)
function addNewNotification(notification) {
if (user && sampleNotifications) {
sampleNotifications.unshift(notification);
// Update badge and content
if (notificationBadge) {
const unreadCount = sampleNotifications.filter(n => n.unread).length;
notificationBadge.textContent = unreadCount;
notificationBadge.style.display = unreadCount > 0 ? 'block' : 'none';
}
if (notificationMenu) {
notificationMenu.innerHTML = generateNotificationContent();
}
}
}
// Function to refresh notifications from server
function refreshNotifications() {
if (!user) return;
fetch('/notifications/get', {
method: 'GET',
headers: {
'Content-Type': 'application/json',
'X-CSRF-TOKEN': document.querySelector('meta[name="csrf-token"]').getAttribute('content')
}
})
.then(response => response.json())
.then(data => {
if (data.success && data.notifications) {
// Update notifications array
sampleNotifications.length = 0;
sampleNotifications.push(...data.notifications);
// Update UI
if (notificationBadge) {
const unreadCount = sampleNotifications.filter(n => n.unread).length;
notificationBadge.textContent = unreadCount;
notificationBadge.style.display = unreadCount > 0 ? 'block' : 'none';
}
if (notificationMenu) {
notificationMenu.innerHTML = generateNotificationContent();
}
}
})
.catch(error => {
console.error('Error refreshing notifications:', error);
});
}
// Auto-refresh notifications every 30 seconds if user is logged in
if (user) {
setInterval(refreshNotifications, 30000);
}
function updateVisitorCount(count) {
const countDiv = document.getElementById('visitorCount');
countDiv.innerHTML = '';
const countString = count.toString();
for (let digit of countString) {
const digitSpan = document.createElement('span');
digitSpan.classList.add('digit');
digitSpan.textContent = digit;
countDiv.appendChild(digitSpan);
}
}
window.onload = function() {
try
{
const currentUrl = window.location.href;
if (currentUrl === "https://examprev.com/contribute-answer-with-examprev")
{
const branchSelect = document.getElementById('branchSelect');
const selectedBranch = branchSelect.value;
fetchQuestions(selectedBranch);
}
console.log("Page loaded successfully without errors.");
}
catch(error)
{
console.error("An error occurred:", error.message);
}
const csrfToken = document.querySelector('input[name="_token"]')?.value;
if (!csrfToken) {
console.error('CSRF token not found');
return;
}
const currentURL = window.location.href;
const formData = new FormData();
// Assuming csrf() is a function that returns the CSRF token.
formData.append('currentUrl', currentURL);
async function fetchVisitorCount() { // Make the function async
try {
const response = await fetch('/getVisitorCount', {
method: 'POST',
headers: {
'X-CSRF-TOKEN': csrfToken
},
body: formData
});
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json(); // Parse the JSON response
updateVisitorCount(data.count); // Assuming the response has a 'count' property
} catch (error) {
console.error("Error fetching visitor count:", error);
updateVisitorCount(12345888); // Fallback if fetch fails
}
}
fetchVisitorCount(); // Call the async function
};
function scrollPagination(direction) {
const container = document.getElementById("paginationContainer");
const scrollAmount = 100; // Adjust scroll distance
container.scrollBy({ left: direction * scrollAmount, behavior: "smooth" });
}
function ensureActivePageVisible() {
const container = document.getElementById("paginationContainer");
const activePage = document.querySelector(".custom-pagination-button.active");
if (activePage) {
const containerRect = container.getBoundingClientRect();
const activePageRect = activePage.getBoundingClientRect();
// Check if the active page is outside the visible scroll area
if (activePageRect.left < containerRect.left || activePageRect.right > containerRect.right) {
container.scrollLeft += (activePageRect.left - containerRect.left) - (container.offsetWidth / 2) + (activePage.offsetWidth / 2);
}
}
}
// Ensure current page is visible when the page loads
document.addEventListener("DOMContentLoaded", ensureActivePageVisible);
document.querySelectorAll(".option").forEach(fieldset => {
fieldset.addEventListener("click", function () {
let questionId = this.getAttribute("data-question-id");
let messageElement = document.getElementById("message-" + questionId);
// Prevent multiple attempts per question
if (document.querySelector(`[data-question-id='${questionId}'].correct`) || document.querySelector(`[data-question-id='${questionId}'].incorrect`)) {
return;
}
let legend = this.querySelector("legend");
legend.style.visibility = "visible";
legend.style.fontFamily = "'Poppins', sans-serif";
if (this.getAttribute("data-correct") === "true") {
this.classList.add("correct");
legend.innerText = "Correct";
legend.classList.add("correct-text");
messageElement.innerText = "Correct! 🎉";
messageElement.style.color = "green";
} else {
this.classList.add("incorrect");
legend.innerText = "Incorrect";
legend.classList.add("incorrect-text");
messageElement.innerText = "Incorrect! ❌ Try again.";
messageElement.style.color = "red";
// Highlight correct answers within the same question
document.querySelectorAll(`[data-question-id='${questionId}'][data-correct='true']`).forEach(correctOption => {
correctOption.classList.add("correct");
let correctLegend = correctOption.querySelector("legend");
correctLegend.style.visibility = "visible";
correctLegend.innerText = "Correct";
correctLegend.classList.add("correct-text");
});
}
});
});
</script></html>