The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5 \ s$. In another $10 \ s$ it will decrease to $\alpha$ times its original magnitude,where $\alpha$ equals

$A$ particle with a restoring force proportional to displacement and a resisting force proportional to velocity is subjected to a driving force $F \sin \omega t$. If the amplitude of the particle is maximum for $\omega = \omega_1$ and the energy of the particle is maximum for $\omega = \omega_2$,then (where $\omega_0$ is the natural frequency of oscillation of the particle):

The amplitude of a damped oscillator is known to decrease to $0.9$ times its original amplitude in $5 \,s$. Approximately, by how many times its original amplitude will it decrease after another $20 \,s$?

What is pure simple harmonic oscillation? Why is it not $100 \%$ possible in practice?

In forced oscillations,a particle oscillates simple harmonically with a frequency equal to

What are damped oscillations? Discuss them using the illustration of a spring.