Oscillations practice · Medium

A sealed spherical ball half filled with a volatile liquid is used as the bob of a pendulum executing simple harmonic motion with period $T_1$. The bob is heated slightly so that the liquid evaporates completely and the period is now found to be $T_2$. Which one of the following is true?

In simple harmonic motion, loss of kinetic energy is proportional to

A particle which is attached to a spring oscillates horizontally with simple harmonic motion with a frequency of $1 / \pi \mathrm{~Hz}$ and total energy of $10 \mathrm{~J}$. If the maximum speed of the particle is $0.4 \mathrm{~ms}^{-1}$, what is the force constant of the spring? What will be the maximum potential energy of the spring during the motion?

Which one of the following is an example of the
force of gravity of the earth acting on a
vibrating pendulum bob?

The motion which is not simple harmonic is

S-I: In a simple harmonic oscillation the average potential energy in one time period is equal to the average kinetic energy in this period.
S-II: The average kinetic energy for one oscillation is equal to half of total mechanical energy.

A body oscillates with a simple harmonic motion having amplitude $0.05 \mathrm{~m}$. At a certain instant, its displacement is $0.01 \mathrm{~m}$ and acceleration is $1.0 \mathrm{~m} / \mathrm{s}^2$. The period of oscillation is

Two simple harmonic motions are represented by ${y_1} = 4\sin \left( {4\pi t + \frac{\pi }{2}} \right)$ and $\;{y_2} = 3\cos \left( {4\pi t} \right)$ The resultant amplitude is

The displacement of a particle along the $x$ axis is given by $x = a{\sin ^2}\omega t$ The motion of the particle corresponds to

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time (in seconds) is

A particle moving on $x$-axis has potential energy $U=2-20 x+5 x^2$ joule along $x$-axis. The particle is released at $x=-3$. The maximum value of $x$ will be ($x$ is in metre)

If the maximum acceleration of a $SHM$ is $\alpha$ and the maximum velocity is $\beta$, then the amplitude of vibration is

In a linear Simple Harmonic Motion (SHM)

(A) Restoring force is directly proportional to the
displacement.

(B) The acceleration and displacement are
opposite in direction.

(C) The velocity is maximum at mean position.

(D) The acceleration is minimum at extreme points.
Choose the correct answer from the options given
below:

Assertion: Pendulum clocks go slow in summer and fast in winter.
Reason: The length of the pendulum used in clock increases in summer.

The displacement of a particle along the ${x}$-axis is given by The motion of the particle corresponds to

There is a large difference between the frequencies of external periodic force and natural frequency of a body. The body will:

The principle involved in the performance of a
spinning-chair circus acrobat is

S-I: In a simple harmonic oscillation the average potential energy in one time period is equal to the average kinetic energy in this period.
S-II: The average kinetic energy for one oscillation is equal to half of total mechanical energy.

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 ω=${\omega _1}$ and the energy of the particle is maximum for ω=${\omega _2}$ then

A particle is attached to a vertical spring and is pulled down a distance $4 \mathrm{~cm}$ below its equilibrium and is released from rest. The initial upward acceleration is $0.5 \mathrm{~ms}^{-2}$. The angular frequency of oscillation is

Statement-I: The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola.

Statement-II: Potential energy and kinetic energy do not vary linearly with position.

Identify the function which represents a periodic motion.

The displacement of a particle is represented by the equation $y=\sin^3 \omega t$. The motion is

Assertion: If a pendulum falls freely, then its time period becomes infinite.
Reason: Free falling body has acceleration, equal to $g$.

The velocity of a particle performing simple
harmonic motion, when it passes through its
mean position is

A light spiral spring supports a 200 g weight at its lower end. It oscillates up and down with a period of 1 s. How much weight (in gram) must be removed from the lower end to reduce the period to 0.5 s?

Assertion (A): The bob of a simple pendulum is a ball full of water. If a fine hole is made at the bottom of the ball, then the time period will no more remain constant.
Reason (R): The time period of simple pendulum does not depend upon mass.

In resonance:

If a body is performing SHM, then its

A) average kinetic energy per cycle is equal to half of its maximum kinetic energy

B) mean speed over a complete cycle is equal to $\frac{2}{\pi}$ times of its maximum speed

Assertion: All small oscillations are simple harmonic in nature.

Reason: Oscillations of spring block system are always simple harmonic whether amplitude is small or large.