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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