The amplitude of a damped oscillator varies with time as $A(t) = A_0 \exp(-bt / 2m)$,where $b = 70 \text{ g/s}$ and $m = 200 \text{ g}$. How long does it take for the mechanical energy to drop to one-fourth of its initial value (in $s$)? (Take $\ln 2 = 0.7$)

$A$ particle is performing simple harmonic motion. If the oscillations are damped oscillations,then the angular frequency is given by:

Sometimes when the speed of a vehicle is increased,its body starts to bounce. Why?

If the amplitudes of a damped harmonic oscillator at times $t=0, t_1$ and $t_2$ are $A_0, A_1$ and $A_2$ respectively,then the amplitude of the oscillator at a time of $(t_1+t_2)$ is

$A$ steady force of $120 \ N$ is required to push a boat of mass $700 \ kg$ through water at a constant speed of $1 \ m/s$. If the boat is fastened by a spring and held at $2 \ m$ from the equilibrium position by a force of $450 \ N$,find the angular frequency of damped $SHM$ in $rad/s$.

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