Oscillations practice · Medium

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 SHM, potential energy of a particle at mean position is $E_1$ and kinetic energy is $E_2$, then

A simple pendulum of length $1 \mathrm{~m}$ and having a bob of mass $100 \mathrm{~g}$ is suspended in a car. moving on a circular track of radius $100 \mathrm{~m}$ with uniform speed $10 \mathrm{~m} / \mathrm{s}$ If the pendulum makes small oscillation in a radial direction about its equilibrium position, then its time period can be given by $T=2 \pi / \alpha^{1 / 4}$ The value of $\alpha$ is

[Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ]

Consider one dimensional motion of a particle of mass $m$. It has potential energy $U=a+b^2$, where ' $a$ ' and ' $b$ ' are positive constants. At origin $(x=0)$ it has initial velocity $v_0$. It performs simple harmonic oscillations. The frequency of the simple harmonic motion depends on

How does the time period of pendulum vary with length

The maximum height of a simple pendulum with respect to the equilibrium position is $\mathrm{h}$ and the maximum velocity of the bob of pendulum is $\mathrm{v}$. Then

In a SHM, when the displacement is one half
the amplitude, what fraction of the total energy
is kinetic?

A simple harmonic oscillation is represented by the equation $y=0.40 \sin \left(\frac{40 t}{7}+0.61\right)$ where $y$ and $t$ are in metre and second respectively. The value of time period is

The kinetic energy of a particle executing S.H.M. is 16 J when it is in its mean position. If the amplitude of oscillations is 25 $cm$ and the mass of the particle is 5.12 kg, the time period of its oscillation is

For a simple pendulum, the graph between $T^2$ and $L$ (where $T$ is the time period and $L$ is the length) is

If $<{E}>$ and $< {U} >$ denote the average kinetic and the average potential energies respectively of mass describing a simple harmonic motion, over one period, then the correct relation is

The displacement of an elastic wave is given by the function $y = 3\sin \omega t + 4\cos \omega t,$ where ‘y’ is in cm and ‘t’ is in second. Then the resultant amplitude in

A linear oscillator of unit mass of force constant $4 \times {10^6}\,\,\frac{N}{m}$ and amplitude $0.01\,\,\,m$ has a total mechanical energy of

A particle hanging from a spring stretches it by $1 \mathrm{~cm}$ at earth's surface. Radius of earth is $6400 \mathrm{~km}$. At a place 800 $\mathrm{km}$ above the earth's surface, the same particle will stretch the spring by:

Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is

The total energy of particle performing SHM depend on

A particle is executing S.H.M with time period $T$ and amplitude $A$. The graphical plot of velocity versus displacement $(v-x)$ of the particle