Oscillations practice · Mixed difficulty

A particle is performing a motion on the $x$-axis with its position given by $x=A+B \sin \omega t.$ The amplitude of particle is

I. In SHM to find time taken in moving from one point to another point, we cannot apply the relation, Time $=\frac{\text { Distance }}{\text { Speed }}$
II. In SHM, speed is constant.
Which of the following statement(s) is/are correct?

A particle executes simple harmonic motion of amplitude $A$. At what distance from the mean position is its kinetic energy equal to its potential energy?

Statement-1: For a particle of mass $1 \mathrm{~kg}$, executing S.H.M., if slope of restoring force vs displacement graph is $=-1$, then the time period of oscillation will be $6.28 \mathrm{~s}$.
Statement-2: If $1 \mathrm{~kg}$ mass is replaced by $2 \mathrm{~kg}$ mass and rest of the information remains same as in statement-1, then the time period of oscillation will remain $6.28 \mathrm{~s}$.

To show that a simple pendulum executes simple harmonic motion, it is necessary to assume that

A particle having mass $10 \mathrm{~g}$ oscillates according to the equation $x=(2.0 \mathrm{~cm}) \sin \left[\left(100 \mathrm{~s}^{-1}\right) t+\pi / 6\right]$. Find the position, the velocity and the acceleration at $t=0.$

(A): Simple harmonic motion is not a uniform motion.
(R): It is the projection of uniform circular motion

The length of the seconds pendulum is 1 m on
the earth. If the mass and diameter of the
planet is half that of the earth then the length
of the seconds pendulum on the planet will be

The maximum acceleration of a particle in SHM is made two times keeping the maximum speed to be constant. It is possible when

A hollow sphere is filled with water through the small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flow out of the hole at the bottom, the period of oscillation will

A particle executes $SHM$. with an amplitude $A$. The ratio of its potential energy to kinetic energy at displacement $y = \frac{A}{2}$ from mean position is

Two masses ${m_1}$ and ${{m_2}}$ are suspended together by a massless spring of constant k. When the masses are in equilibrium, ${{m_1}}$ is removed without disturbing the system. Then the angular frequency of oscillation of ${{m_2}}$ is

Assertion: The amplitude of oscillation can never be infinite.
Reason: The energy of oscillator is continuously dissipated.

A body starting at $t=0$ from origin and oscillates simple harmonically with a period of 4s. After what time will its kinetic energy by $75 \%$ of its total energy.

The acceleration $d^2 x / d t^2$ of a particle varies with displacement $x$ as $\frac{d^2 x}{d t^2}=-k x$ where $k$ is a constant of the motion. The time period $T$ of the motion is equal to

A simple pendulum oscillates in air with time period $T$ and amplitude $A$. As the time passes:

A pendulum clock has time period $T$ at normal room temperature. If $T_s$ and $T_w$ are the time periods of the same pendulum in summers and winters respectively, then;

Assertion: The graph between velocity and displacement for a harmonic oscillation is a straight line.
Reason: Velocity changes uniformly with displacement in simple harmonic motion.

What is the number of degrees of freedom for an oscillating simple pendulum?

A man measures the period of simple pendulum inside a stationary lift and finds it to be $\mathrm{T}$ second. If the lift accelerates downwards with acceleration of $\mathrm{g} / 4$, the period of oscillation will be-

A pendulum clock is placed on the moon, where object weighs only one-sixth as much as on earth, how many seconds the clock tick out in an actual time of 1 minute the clock keeps good time on earth?

Two pendulum oscillate with a constant phase difference of $45^{\circ}$ and same amplitude. If the maximum velocity of one of them is $v$ and that of other is $v+x$, then the value of $x$ will be

A circular disc rotating with frequency $f_0=1.3$ rev/sec comes to a stop in 30 seconds. The approximate angular acceleration is:

I. Average kinetic energy in one oscillation during SHM of a body is $\frac{1}{4} m \omega^2 A^2$.

II. Maximum kinetic energy is $\frac{1}{2} m \omega^2 A^2$.

Which of the following statement(s) is/are correct?

Which one of the following is the correct relation between frequency $\mathrm{f}$ and angular frequency $\omega$ ?

The displacement of two particles of same mass executing simple harmonic motions are $x_1=16 \sin \left(10 t+\frac{\pi}{2}\right)$ and $x_2=25 \cos (\omega t)$ respectively.
The value of ' $\omega$ ' for which the energies of both the particles remain the same is

A spring compressed by $0.2 \mathrm{~m}$ develops a restoring force of $25 \mathrm{~N}$. A body of mass $5 \mathrm{~kg}$ is placed over it. Deduce:
(i) force constant of the spring
(ii) the depression of the spring under the weight of the body and
(iii) the period of oscillation, if the body is disturbed.
Take $g=10 \mathrm{~N} \mathrm{~kg}^{-1}$.

The displacement of a particle from its mean position (in $m$ ) is given by $y=$ $0.4 \sin (5 \pi t+2.5 \pi) \cos (5 \pi t+2.5 \pi)$. The motion of the particle is

All oscillatory motions are necessarily periodic motions but:

A particle is subjected to three $SHMs$

$X_1=3 \sin \omega t$

$X_2=4 \cos \omega t$

$X_3=6 \sin (\omega t+\pi)$

Where $X$ is in metre. The resultant amplitude of particle is