Oscillations practice · Mixed difficulty

Two equations of two S.H.M. are $y = a\sin \left( {\omega t - \alpha } \right)$ and $y = b\cos \left( {\omega t - \alpha } \right)$ The phase difference between the two is

The equation of linear simple harmonic motion is $x=8 \cos (12 \pi t)$ where $x$ is in $\mathrm{cm}$ and $t$ is in second. The initial phase angle is:

Two pendulums of time periods $3 \mathrm{~s}$ and $7 \mathrm{~s}$ respectively, start oscillating simultaneously from two opposite extreme positions. After how much time they will be in same phase?

Statement I When a wave goes from one medium to other, average power transmitted by the wave may change.
Statement II Due to a change in the medium, amplitude, speed, wavelength and frequency of the wave may change.

It is impossible for two oscillators, each
executing simple harmonic motion, to remain
in phase with each other if they have different

During the swinging of simple pendulum,

The motion of a particle is expressed by the equation acc. a $=-$ bx where $\mathrm{x}$ is displacement from equilibrium position and $b$ is constant. What is the periodic time?

Displacement-time equation of a particle executing SHM is, $x = 4\sin \omega t + 3\sin \,\,(\omega t + \pi /3)$ Here $x$ is in centimeter and t in second. The amplitude of oscillation of the particle is approximately

A particle of mass 1 kg is moving in SHM with an amplitude 0.02 m and a frequency of 60 Hz. The maximum force in newton acting on the particle is

Which of the following characteristics does not change� due to the damping of simple harmonic motion?

The maximum velocity of a simple harmonic motion represented by $y = 3\sin \left[ {100t + \frac{\pi }{6}} \right]$ is given by

The quantity which does not vary periodically
for a particle performing S.H.M. is

A block whose mass is $650 \mathrm{~g}$ is fastened to a spring whose spring constant is $65 \mathrm{~N} / \mathrm{m}$. The block is pulled a distance $x=11 \mathrm{~cm}$ from its equilibrium position at $x=0$ on a frictionless surface and released from rest at $t=0$. The maximum velocity of the vibrating block is

The average acceleration of a particle performing SHM over one complete oscillation is

The mass of a bob, suspended in a simple pendulum, is halved from the initial mass, its time period will:

Two springs have spring constants ${K_A}$ and ${K_B}$ and $\;{K_A} > {K_B}$ The work required to stretch them by same extension will be

A simple harmonic wave having an amplitude a and time period T is represented by the equation $y = 5\sin \pi \left( {t + 4} \right)m$ then the value of amplitude (a) in (m) and time period (T) in second are

The height of a swing changes during its motion from 0.1 $m$ to 2.5 $m$. The minimum velocity of a boy who swings in this swing is

Assertion: In $x=A \cos \omega t, x$ is the displacement measured from extreme position.

Reason: In the above equation $x=A$ at time $t=0$.

How does time period of a pendulum very with length?

Which of the following quantities are always positive in a simple harmonic motion?

The amplitude of a simple harmonic oscillator is 2 cm. At certain instant its PE and KE are equal. The displacement from mean position at that instant is

When a particle executing SHM oscillates with a frequency $v$, then the kinetic energy of the particle

Ratio of kinetic energy at mean position to potential energy at A⁄2 of a particle performing SHM

A simple pendulum is vibrating in an
evacuated chamber. It will oscillate with ––––

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°

Assertion: When a particle is at extreme position performing SHM, its momentum is equal to zero.
Reason: At extreme position the velocity of particle performing SHM is equal to zero.

A simple harmonic oscillator has an amplitude of $0.5 \mathrm{~m}$ and a time period of 2 seconds. What is the magnitude of acceleration when it is displaced from the mean position by $0.25 \mathrm{~m}$ ?

A simple pendulum has a length $l$ . The inertial and gravitational masses of the bob are ${m_i}$ and ${m_g}$ respectively. Then the time period $T$ is given by

A block of mass $m$ attached to a massless spring is performing oscillatory motion of amplitude $A$ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system becomes $fA.$ The value of $f$ is