Aerospace Engineering Gate 2017 Questions with Answer

Ques 40 GATE 2017

Consider the initial value problem:

d²y/dt²+4dy/dt+6y=f(t); y(0)=2, (dy/dt)_t=0=1

If Y(s)=∫₀^∞y(t)e^-stdt and F(s)=∫₀^∞f(t)e^-stdt are the Laplace transforms of y(t) and f(t) respectively, then Y(s) is given by:

Ques 41 GATE 2017

Let u(x,t) denote the displacement of a point on a rod. The displacement satisfies the following equation of motion:
∂²u/∂t²-25∂²u/∂x²=0 , 0
with u(x,0)=0.01sin(10πx), ∂u/∂t(x,0)=0; u(0,t)=0, u(1,t)=0 The value of u(0.25,1) is _______ (in three decimal places).

Ques 42 GATE 2017

The equation x² d²y/dx²+5x dy/dx+4y=0 has a solution y(x) that is:

Ques 43 GATE 2017

The ninth and the tenth of this month are Monday and Tuesday

Ques 44 GATE 2017

It is _______ to read this year's textbook _______ the last year's.

Ques 45 GATE 2017

If you are looking for a history of India. or for an account of the rise and fall of the British Raj. or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia. you will not find it in these pages: for though I have spent a lifetime in the country. I lived too near the seat of events and was too intimately associated with the actors. to get the perspective needed for the impartial recording of these matters."

Which of the following statements best reflects the author's opinion?

Ques 46 GATE 2017

A 2-DOF undamped spring-mass system with two masses and two springs has natural frequencies ω₁=0.79 rad/s and ω₂=1.538 rad/s. The mode shapes for the system are given by φ₁=[0.732 1]^T and φ₂=[-2.73 1]^T If the first mass is displaced by 1 cm, the minimum displacement in cms to be given to the second mass to make the system vibrate in first mode alone is _______ (in three decimal place).

Ques 47 GATE 2017

An aircraft landing gear can be idealized as a single degree of freedom spring-mass-damper system. The desirable damping characteristics of such a system is:

Ques 48 GATE 2017

A single degree of freedom spring-mass system of natural frequency 5 Hz is modified in the following manners:

Case 1: Viscous damping with damping ratio ζ=0.2 is introduced in parallel to the spring.
Case 2: The original undamped spring-mass system is moved to a surface with coefficient of friction, μ=0.01.

The ratio of the damped natural frequency for the cases 1 and 2 is given by _______ (in three decimal places).

Ques 49 GATE 2017

An aircraft model was tested in a low speed wind-tunnel (Reynolds number =2×10⁶ based on wing mean chord). The variation of pitching moment coefficient (C_m) with angle of attack (α) for two elevator deflections (δ_e) as recorded during this test is presented below.

Ques 50 GATE 2017

The roots obtained by solving longitudinal characteristic equations of motion for a statically stable aircraft are given below:

λ_.1,2=-0.02±0.30i, λ_.3,4=-2.00±2.50i, where i=√-1

The undamped short-period longitudinal natural frequency (radians/sec) and damping ratio, in that order, are close to

Ques 51 GATE 2017

A conventional aircraft was analyzed to estimate the contribution of wing towards C_m0 (C_m at α=0) of the whole aircraft. The wing was installed with zero setting angle along the fuselage reference line. Further, the wing was laid such that X¯_ac,w=0.3 and X¯_cg,aircraft=0.4. X¯_ac,w and X¯_cg,aircraft are the non-dimensional distances, from the leading edge of the wing. of the aerodynamic center of the wing and center of gravity of the aircraft respectively. The wing had the following aerodynamic characteristics:

C_L0=0.20 and C_mac,wing=-0.02.

The numerical value of C_m0,w (contribution of the wing to C_m0) about the CG of the aircraft is _______ (in two decimal places).

Ques 52 GATE 2017

The natural frequency of the system suspended by two identical springs of stiffness k as shown in the figure is given by ω_n=a√(k/m) for small displacement. Both the springs make an angle of 45° with the horizontal. The value of a is _______ (in two decimal places).