Oscillations practice · Medium

A heavy sphere of mass $m$ is suspended by string of length $l$. The sphere is made to revolve about a vertical line passing through the point of suspension in a horizontal circle such that the string always remains inclined to the vertical at an angle $\theta$. What is its period of revolution?

The acceleration of a particle in S.H.M. is

A block of mass one $\mathrm{kg}$ is fastened to a spring with a spring constant $50 \mathrm{~Nm}^{-1}$. The block is pulled to a distance $x=10 \mathrm{~cm}$ from its equilibrium position at $x=0$ on a frictionless surface from rest at $t=0$. Write the expression for its $x(t)$ and $v(t)$.

Which one of the following is not a periodic motion?

A particle starts S.H.M. from the mean position. Its amplitude is a and total energy ${E}$. At one instant 5 its kinetic energy is $3 {~E} / 4$, its displacement at this instant is

Assertion: Every periodic motion is not always a simple harmonic motion.
Reason: The motion governed by the force law $F = −kx$ is simple harmonic.

The acceleration of particle executing SHM
when it is at mean position is

Two particles execute simple harmonic motion of the same amplitude and frequency along the same straight line. They pass one another when going in opposite directions and each time their displacement is half the amplitude. The phase difference between them is

A particle oscillates simple harmonically with a period of $16 \mathrm{~s}$. Two second after crossing the equilibrium position its velocity becomes $1 \mathrm{~m} / \mathrm{s}$. The amplitude is

The equation of a simple harmonic motion is $x=0.34 \cos (3000 t+0.74)$, where $x$ and $t$ are in $\mathrm{mm}$ and second, respectively. The frequency of the motion (in $\mathrm{Hz}$) is

A particle is executing SHM of period 24 $x$ and of amplitude 41 cm with O as equilibrium position. The minimum time in seconds taken by the particle to go from P to Q. where OP = -9 cm and OQ =40 cm is

S-I: In SHM, total mechanical energy can be negative also.
S-II: Potential energy is always negative.

The equation of a simple harmonic motion is given by $y=6 \sin 10 \pi t+8 \cos 10 \pi t$, where $y$ is in cm and $t$ in sec. Determine the period and initial phase.

A particle executing simple harmonic motion has an amplitude of $6 \mathrm{~cm}$. Its acceleration at a distance of $2 \mathrm{~cm}$ from the mean position is $8 \mathrm{cms}^{-2}$. The maximum speed of the particle is

Which of the following expressions corresponds to simple harmonic motion along a straight line, where $x$ is the displacement and $a, b, c$ are positive constants?

Statement-I: In simple harmonic motion $A$ is the amplitude of oscillation. If $t_1$ be the time to reach the particle from mean position to $\frac{A}{\sqrt{2}}$ and $t_2$ the time to reach from $\frac{A}{\sqrt{2}}$ to $A$. Then $t_1=\frac{t_2}{\sqrt{2}}$

Statement-II: Equation of motion for the particle starting from mean position is given by $x= \pm \mathrm{A} \sin \omega \mathrm{t}$ and of the particle starting from extreme position is given by $x= \pm$ $A\cos \omega t$

The equation $y={a \cos} 2 \omega t+a \sin 2 \omega t$ is

For a body executing SHM
A. potential energy is always equal to its kinetic energy.
B. average potential and kinetic energy over any given time interval are always equal.
C. sum of the kinetic and potential energy at any point of time is constant.
D. average kinetic energy is one time period is equal to average potential energy in one time period.
Choose the most appropriate option from the options given below.

Periodic motion is one which:

When the bob of a simple pendulum swings, the work done by tension in the string is

A pendulum clock gains 5 seconds per day at a temperature of $15^{\circ} \mathrm{C}$ and loses 10 seconds per day at a temperature $30^{\circ} \mathrm{C}$. At what temperature, the pendulum clock will neither gain nor lose time?

The necessary condition for the bob of a
pendulum to execute SHM is

Two pendulums of lengths 1m and 1.21m respectively start swinging together with same amplitude. The number of vibrations that will be executed by the longer pendulum before the two will swing together again are

A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is $\frac{2}{{\sqrt 5 }}$ After how many collisions the amplitude of vibration will become less than 60°

Which type of oscillations are damped oscillations?

In the case of conical pendulum, if $\mathrm{T}$ is the tension in the string and $\theta$ is the semi vertical angle of cone, then the component of tension which balances the centrifugal force in equilibrium position is

The time period of a simple pendulum, when it is made to oscillate on the surface of moon

A particle is executing S.H.M. Then the graph of acceleration as a function of displacement is

A simple pendulum performs simple harmonic motion about $x=0$ with an amplitude $A$ and time period $T$. The speed of the pendulum at $x=\frac{A}{\sqrt{3}}$ will be

Which of the following equation does not represent a SHM?