List of top Propulsion Questions on Vibration Analysis asked in GATE AE

A damper with damping coefficient, \( c \), is attached to a mass of 5 kg and spring of stiffness 5 kN/m as shown in the figure. The system undergoes under-damped oscillations.
If the ratio of the 3rd amplitude to the 4th amplitude of oscillations is 1.5, the value of \( c \) is _________ Ns/m (rounded off to the nearest integer).

A uniform rigid prismatic bar of total mass \( m \) is suspended from a ceiling by two identical springs as shown in the figure.
Let \( \omega_1 \) and \( \omega_2 \) be the natural frequencies of mode I and mode II respectively (with \( \omega_1<\omega_2 \)).
The value of \( \omega_2/\omega_1 \) is _________ (rounded off to one decimal place).