A precision instrument package $)=(1kg$ needs to be mounted on a surface vibrating at $60$ Hz $.$ It is desired that only $5\%$ of the base surface vibration amplitude be transmitted to the instrument. Assume that the isolation is designed with its natural frequency significantly less than $60$ Hz $,$ so that the effect of damping may be ignored. The stiffness $($in $k\frac{N}{m})$ of the required mounting pad is

a$.5\mathrm{.}4$

b$.6\mathrm{.}8$

c$.9\mathrm{.}2$

d$.8\mathrm{.}3$

e$.$ None of the above

In a spring$-$mass system the mass is m and the spring constant is k $.$ The critical damping coefficient of the system is $0\mathrm{.}1k\frac{g}{s}.$ In another spring mass system, the mass is $2$ m and the spring constant is $8$ k $.$ The critical damping coefficient $($in $k\frac{g}{s})$ of this system is

a$.0\mathrm{.}1$

b$.0\mathrm{.}2$

c$.0\mathrm{.}3$

d$.0\mathrm{.}4$

e$.$ None of the above

A single$-$degree$-$freedom spring$-$mass is subjected to a sinusoidal force of $10$ N amplitude and frequency $$ along the axis of the spring. The stiffness of the spring is $150\frac{N}{m},$ damping factor is $0\mathrm{.}2$ and undamped natural frequency is $10.$ At steady state, the amplitude of vibration $($in m $)$ is approximately

a$.0\mathrm{.}05$

b$.0\mathrm{.}07$

c$.0\mathrm{.}70$

d$.0\mathrm{.}90$

e$.$ None of the above

Which of the following statements are TRUE for damped vibrations?

P$.$ For a system having critical damping, the value of the damping ratio is unity and system does not undergo a vibratory motion.

Q$.$ Logarithmic decrement method is used to determine the amount of damping in a physical system.

R$.$ In case of damping due to dry friction between moving surfaces resisting force of constant magnitude acts opposite to the relative motion.

S$.$ For the case of viscous damping, drag force is directly proportional to the square of relative velocity.

a$.$ P and Q only

b$.$ P and S only

c$.$ P$,$ Q and R only

d$.$ Q and S only

e$.$ None of the above