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 one third in $2 \, s$. If its amplitude after $6 \, s$ is $1/n$ times the original amplitude,then the value of $n$ 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 $750 \;kg$.

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

When an external force with angular frequency $\omega_d$ acts on a system of natural angular frequency $\omega$,the system oscillates with angular frequency $\omega_d$. The condition for the amplitude of oscillations to be maximum is

The mechanical energy of a damped oscillator becomes half of its initial energy in $4 \ s$. In another $t \ s$,its mechanical energy becomes $12.5 \%$ of its initial mechanical energy. Then $t=$ (in $s$)