In damped oscillation,the graph between velocity $(V)$ and position $(x)$ will be:

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:

Write the practical examples of resonance.

$A$ block of mass $1 \, kg$ attached to a spring is made to oscillate with an initial amplitude of $12 \, cm$. After $2 \, minutes$ the amplitude decreases to $6 \, cm$. Determine the value of the damping constant $b$ for this motion. (Take $\ln 2 = 0.693$)

Write the equation of angular frequency and amplitude for damped oscillation.

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: