The graph between velocity and position for a damped oscillation will be:

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

In a time of $2 \ s$,the amplitude of a damped oscillator becomes $\frac{1}{e}$ times its initial amplitude $A$. In the next two seconds,the amplitude of the oscillator is

$A$ simple pendulum oscillates in air with time period $T$ and amplitude $A$. As the time passes,

For the damped oscillator shown in the figure,the mass $m$ of the block is $200 \; g$,$k = 90 \; N m^{-1}$,and the damping constant $b$ is $40 \; g s^{-1}$. Calculate:
$(a)$ the period of oscillation,
$(b)$ the time taken for its amplitude of vibrations to drop to half of its initial value,and
$(c)$ the time taken for its mechanical energy to drop to half its initial value.

Write the equation of angular frequency and amplitude for damped oscillation.