Damped and Forced Harmonic Motion

In a free oscillation,what happens to the amplitude,frequency and energy of the oscillating body?

In case of a forced oscillation, the resonance peak becomes very sharp when the

The vibrations that can continue even after the external force is removed are called free vibrations or natural vibrations.

Natural frequency of a body depends on the shape, size, and _____ (elasticity/intensity) of the body.

Explain why simple motion of pendulum stop after some time?

Define damped harmonic motion.

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.

When a body of natural frequency $n$ is subjected to the external force vibrating with frequency $p$, the body vibrates with frequency $p$ under steady state with an amplitude which depends upon

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

A metal wire of linear mass density of $9.8 g m^{-1}$is stretched with a tension of kg-wt between two rigid supports 1 m apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance when carrying an alternating current of frequency n. the frequency n of the alternating sources is

A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force.

$F=F_0\sin \omega t$

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

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,

If the differential equation given by

$\frac{d^{2}y}{d{t}^2}+2k\frac{dy}{dt}+{\omega }^{2}y=F_0\mathrm{ sin }pt$

Describes the oscillatory motion of body in a dissipative medium under the influence of a periodic force, then the state of maximum amplitude of the oscillation is a phenomena of

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