Four pendulums $A, B, C$ and $D$ are hung from the same elastic support as shown in the figure. $A$ and $C$ are of the same length,while $B$ is shorter than $A$ and $C$,and $D$ is longer than $A$. If $A$ is given a displacement,then at steady state:

The amplitude of a damped oscillator becomes half in $1 \text{ minute}$. The amplitude after $3 \text{ minutes}$ will be $\frac{1}{X}$ times the original,where $X$ is

You are riding in an automobile of mass $3000\; kg$. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags $15\; cm$ when the entire automobile is placed on it. Also,the amplitude of oscillation decreases by $50 \%$ during one complete oscillation. Estimate the values of
$(a)$ the spring constant $k$ and
$(b)$ the damping constant $b$ for the spring and shock absorber system of one wheel,assuming that each wheel supports $750 \;kg$.

In forced oscillation of a particle,the amplitude is maximum for a frequency $\omega_{1}$ of the driving force,while the energy is maximum for a frequency $\omega_{2}$ of the driving force. Then:

The amplitude of a damped oscillator becomes $\left(\frac{1}{3}\right)$ of its original amplitude in $2 \ s$. If its amplitude after $6 \ s$ becomes $\left(\frac{1}{n}\right)$ times the original amplitude,the value of $n$ is ($n$ is a non-zero integer).

In damped $SHM$,the $SI$ unit of damping constant is