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

$A$ block of mass $100 \,g$ is connected to an elastic spring of spring constant $450 \,N m^{-1}$ and oscillates vertically. The block-spring system is in a viscous surrounding medium with a damping constant $b = 69.3 \,g \,s^{-1}$. Calculate the time in which the amplitude of oscillations drops to half of its initial value. (Take $\ln 2 = 0.693$) (in $\,s$)

Why is absolutely pure simple harmonic motion not possible?

To understand resonance,describe the experiment of oscillations of five pendulums.

Resonance is an example of

In damped oscillations,the damping force is directly proportional to the speed of the oscillator. If the amplitude becomes half of its initial value $A_0$ in $1 \, s$,then after $2 \, s$,the amplitude will be: