Which of the diagrams shown in the figure represents the variation of total mechanical energy of a pendulum oscillating in water as a function of time?

$A$ block of mass $200 \, g$ is executing $SHM$ under the influence of a spring with spring constant $K = 90 \, N \, m^{-1}$ and a damping constant $b = 40 \, g \, s^{-1}$. The time elapsed for its amplitude to drop to half of its initial value is ...... $s$ (Given $\ln \frac{1}{2} = -0.693$).

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

When an oscillator completes $100$ oscillations,its amplitude is reduced to $\frac{1}{3}$ of its initial value. What will be its amplitude after it completes $200$ oscillations?

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 $750 \;kg$.

The amplitude of a damped oscillator becomes half in $1 \text{ minute}$. The amplitude after $3 \text{ minutes}$ will be $\frac{1}{X}$ times the original,where $X$ is