Aerospace Engineering > GATE 2021 > Free Vibrations
A two-degree of freedom spring-mass system undergoing free vibration with generalized coordinates x1 and x2 has natural frequencies ω1 = 233.9 rad/s and ω2 = 324.5 rad/s, respectively. The corresponding mode shapes are φ1 = [1, -3.16] and φ2 = [1,3.16]. If the system is disturbed with certain deflections and zero initial velocities, then which of the following statement(s) is/are true?
A
An initial deflection of x1(0) = 6.32 cm and x2(0) = -3.16 cm would make the system oscillate with only the second natural frequency.
B
An initial deflection of x1(0) = 2 cm and x2(0) = -6.32 cm would make the system oscillate with only the first natural frequency.
C
An initial deflection of x1(0) = 2 cm and x2(0) = -2 cm would make the system oscillate with a linear combination of first and second natural frequencies.
D
An initial deflection of x1(0) = 1 cm and x2(0) = -6.32 cm would make the system oscillate with only the first natural frequency.

Correct : b,c

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Related Topics

spring mass system two degree of freedom GATE Aerospace Engineering 2021 vibration analysis mode shapes natural frequencies system response aerospace engineering gate vibration system spring mass system oscillation GATE 2021 Q32

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