Oscillations practice · Medium

Assertion: We can call circular motion also as simple harmonic motion.

Reason: Angular velocity in uniform circular motion and angular frequency in simple harmonic motion have the same meanings.

For definite length of wire, if the weight used for applying tension is immersed in water, then frequency will

The displacement of a particle executing periodic motion is given by $y=4 \cos ^2(t / 2) \sin (1000 t)$. Find the independent constituent SHM's.

Energy of particle executing SHM depends upon

A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of $40 {~cm}$. The block just loses contact with the plank when the later is momentarily at rest, then

The system that returns to equilibrium as quickly as possible without oscillating is

$x(t)=A \cos (\omega t+\phi)$ is the equation of simple harmonic motion. In this equation ' $\phi$ ' is called

S-I: If the amplitude of the oscillation is doubled the maximum kinetic energy becomes four times.
S-II: If the amplitude of the oscillation is doubled the minimum potential energy also becomes four times.

Instantaneous acceleration (in ${ms}^{-2}$ ) of a particle executing S.H.M is given by $a=-\frac{\pi}{4} \sin \left(\frac{\pi}{4} t-\frac{\pi}{6}\right)$. The maximum speed of the particle will occur first time at

A particle starts executing simple harmonic motion (SHM) of amplitude $a$ and total energy $E$. At any instant, its kinetic energy is $\frac{{3E}}{4}$, then its displacement $y$ is given by

Resonance is an example of:

A particle executes linear S.H.M. with amplitude $4 \mathrm{~cm}$. The magnitude of velocity and acceleration is equal when it is at $3 \mathrm{~cm}$ from mean position. The time period is

The period of a simple pendulum inside a stationary lift is$T$. The lift accelerates upwards with an acceleration of g⁄3. The time period of pendulum will be

Assertion (A): The graph of PE and KE of a particle is SHM with respect to position is a parabola.
Reason (R): This because PE and KE do not vary linearly with position.

The time period of a simple pendulum on a freely moving artificial satellite is

Which of the following quantities are always negative in a S.H.M
$(\overrightarrow F = \,force,\,\,\overrightarrow V \, = \,velocity,\,\,\overrightarrow a \, = \,acceleration,\,\,\overrightarrow r \, = \,displacement)$

Assertion: The graph of total energy of a particle in SHM. wrt, position is a straight line with zero slope.
Reason: Total energy of particle in SHM remains constant throughout its motion.

A particle of mass $4 {~cm}$ is executing oscillations about the origin on the $X$-axis. Its potential energy is $U(x)=k|x|^3$, where $k$ is a positive constant. If the amplitude of oscillation is $4 {~cm}$, then its time period $T$ will be proportional to

Particle moves on the $\mathrm{x}$-axis according to the equation $\mathrm{x}=$ $\mathrm{A}+\mathrm{B} \sin \omega \mathrm{t}$. The motion is simple harmonic with amplitude.

How much revolution does the engine make during the time when a motor wheel with angular speed is increased from $720 \mathrm{~rpm}$ to $2820 \mathrm{~rpm}$ in 14 seconds?

An object of mass $0.2 \mathrm{~kg}$ executes $\mathrm{SHM}$ along $x$-axis with frequency of $\frac{25}{\pi}$ Hz. At the position $x=0.04 \mathrm{~m}$, the object has kinetic energy of $0.5 \mathrm{~J}$ and potential energy of $0.4 \mathrm{~J}$. The amplitude of oscillation is

The amplitude of vibration of a particle is given by ${a_m} = ({a_0})/(a{\omega ^2} - b\omega + c);$ where ${a_0},a,b$ and c are positive. The condition for a single resonant frequency is

The height of liquid column in a $U$ tube is 0.3 meter. If the liquid in one of the limbs is depressed and then released, then the time period of liquid column will be-

If the ratio of the acceleration due to gravity on the surface of earth to that on the surface of the moon is $6: 1$, then the ratio of the periods of a simple pendulum on their surface is

If two springs $A$ and $B$ with spring constant $2 \mathrm{~k}$ and $\mathrm{k}$, are stretched separately by same suspended weight, then the ratio between the work done in stretching $A$ and $B$ is

The phase difference between two $SHMs$ $y_1=10 \sin \left(20 t+\frac{\pi}{6}\right)$ and $y_2=20 \cos \left(20 t-\frac{\pi}{6}\right)$ is

A horizontal platform vibrates with simple harmonic motion in the horizontal direction with a period 2 s. A body of mass 0.5 kg is placed on the platform. The coefficient of static friction between the body and platform is 0.3. What is the maximum frictional force on the body when the platform is oscillating with amplitude 0.2 m? Assume ${\pi ^2} = 10 = g$.

A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes $\left(\frac{1}{4}\right)^{\text {th }}$ of the original in time ' $t$ ' and ' $n$ ' revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are (Angular retardation is uniform)

A body is executing simple harmonic motion. When the displacements from the mean position is $4 {~cm}$ and $5 {~cm}$, the corresponding velocities of the body are $10 {~cm} / {sec}$ and $8 {~cm} / {sec}$. Then the time period of the body is

The total mechanical energy of a spring-mass system in simple harmonic motion is $E=\frac{1}{2} m \omega^2 A^2$. Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude $A$ remains the same. The new mechanical energy will