In the case of a forced vibration,the resonance curve becomes very sharp when the

$A$ $3 \ kg$ sphere dropped through air has a terminal speed of $25 \ m/s$. (Assume that the drag force is $F_d = -bv$). Now suppose the sphere is attached to a spring of force constant $k = 300 \ N/m$,and that it oscillates with an initial amplitude of $20 \ cm$. What is the angular frequency of its damped $SHM$? ..... $rad/s$

The amplitude of a simple pendulum,oscillating in air with a small spherical bob,decreases from $10 \ cm$ to $8 \ cm$ in $40 \ s$. Assuming that Stokes' law is valid,and the ratio of the coefficient of viscosity of air to that of carbon dioxide is $1.3$. The time in which the amplitude of this pendulum will reduce from $10 \ cm$ to $5 \ cm$ in carbon dioxide will be close to ..... $s$ $(\ln 5 = 1.601, \ln 2 = 0.693)$

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

Why is absolutely pure simple harmonic motion not possible?

Explain the behaviour of the oscillator when the driving frequency is close to the natural frequency in small damped oscillation and define resonance.