Damped Oscillations

Explain the role of shock absorbers in car.

Explain that in damped SHM, the energy is constantly dissipated to the surrounding.

Which of the following differential equations represents a damped harmonic oscillator?

When a damped harmonic oscillator completes $100$ oscillations, its amplitude is reduced to ${\left(\frac{1}{3}\right)}^{\mathrm{rd} }$ of its initial value. What will be its amplitude when it completes $200$ oscillations?
 

Compare the effect of damping on the resonance vibration of sonometer and of the air column.

A damped oscillator consists of a spring-mass system with mass $2 \mathrm{kg}$ and spring of spring constant $10 \mathrm{N} {\mathrm{m}}^{-1}$. The damping force is given by $F=-b\left(\frac{\mathrm{d}x}{dt}\right)$ where $b=280 \mathrm{g} {\mathrm{s}}^{-1}.$ The time required for the amplitude of the oscillations to reduce to one-fourth ${\left(\frac{1}{4}\right)}^{th}$ of its initial value is: (Assume $\ln 2=0.7$)

In the following a statement of Assertion is followed by a statement of Reason.

Assertion: In damped oscillations, the oscillator experiences both conservative and non-conservative forces.

Reason: In damped oscillations mechanical energy of oscillator decreases with time.

In an experiment to find the loss of energy with respect to time in the case of a swinging simple pendulum, the graph between the square of amplitude and time is best represented by

The amplitude of damped oscillator becomes $\frac{1}{3}\mathrm{rd}$ of the original in $2 \mathrm{s}$. Its amplitude after $6 \mathrm{s}$ is $\frac{1}{n}$ times the original. Then, $n$ is equal to,

The amplitude of a damped oscillator becomes ${\left(\frac{1}{3}\right)}^{\mathrm{rd}}$ in $2 \mathrm{s}$. If its amplitude after $6 \mathrm{s}$ is $\frac{1}{n}$ times the original amplitude, the value of $n$ is

The angular frequency of the damped oscillator is given by, $\omega =\sqrt{\left(\frac{\text{k}}{\text{m}}-\frac{{\text{r}}^2}{4{\text{m}}^2}\right)}$ where k is the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio $\frac{{\text{r}}^2}{\text{mk}}$ is 8%, the change in time period compared to the undamped oscillator is approximately as follows :

A simple pendulum after some time becomes slow in motion and finally stops due to

The equation  $\frac{d^{2}y}{{\mathit{\text{dt}}}^2}+\frac{\mathit{\text{bdy}}}{\mathit{\text{dt}}}+{\omega }^{2}y=0$ represents the equation of motion for a