Oscillations practice · Mixed difficulty

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

A vertical spring block system is made to oscillate.
Statement-1: Its time period on earth is more than that on the moon.
Statement-2: Its extension on earth (in equilibrium) is more than that on the moon.

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?

A simple pendulum executing S.H.M. about $x=0$ with period $T$ and amplitude $A$. Its speed when at a distance $\frac{A}{2}$ is

A man measures the period of a simple pendulum inside a stationary lift and finds it to be $T$ second. If the lift accelerates upwards with an acceleration g/4, then the period of pendulum will be

A particle free to move along the $x$ -axis has potential energy given as $U\left( x \right) = k\left[ {1 - \exp \left( { - {x^2}} \right)} \right]\,\,\,\,\,\,\left( {\mathrm{for} - \infty \le + \infty } \right)$ Where k is a positive constant of appropriate dimensions. Then

On being displaced, a liquid contained in a $U$-tube executes:

Statement-1: When a girl sitting on a swing stands up, the periodic time of the swing will increase.
Statement-2: In standing position of a girl, the length of the swing will decrease.

If the time period of a 2m long simple pendulum is 2s, the acceleration due to gravity at the place, where pendulum is executing SHM is

Assertion: A harmonic oscillator has two degrees of freedom.
Reason: It has both kinetic energy and potential energy.

A spring of spring constant $5 \times 10^3 \mathrm{~N} / \mathrm{m}$ is stretched by $4 \mathrm{~cm}$ from its outstretched position. Then the work required to stretch it further by $4 \mathrm{~cm}$ is

Assertion: Path of a particle in SHM is always a straight line.

Reason: All straight line motions are not simple harmonic.

A mass $m$ attached to a spring oscillates with a time period $4 \mathrm{~s}$. If the mass is increased by $1 \mathrm{~kg}$, then period increases by $1 \mathrm{~s}$. Its initial mass is

A mass $M$ is suspended from a light spring. An additional mass $m$ is added and displaces the spring further by a distance $X$. Now the combined mass will oscillate on the spring with period

A simple pendulum suspended from the roof of a lift oscillates with frequency $n$ when the lift is at rest. If the lift falls freely under gravity, its frequency of oscillation becomes:-

When the amplitude of a body executing SHM become twice what happens?

Assertion: The energy of the system is dissipated continuously in damped oscillations.
Reason: The oscillations remain approximately periodic for small damping.

In a simple pendulum, the period of oscillation $T$ is related to length of the pendulum $l$ as