Oscillations practice · Mixed difficulty

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

Molten-wax of mass $m$ drops on a block of mass $M$, which is oscillating on a frictionless table. Select the correct option.

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

Two particles are executing simple harmonic motion. At an instant of time $t$, their displacements are $y_1=A \cos (\omega t)$ and $y_2=A \sin (\omega t)$
Then, the phase difference between $y_1$ and $y_2$ is

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

A particle is executing simple harmonic motion. Its displacement to amplitude ratio when its kinetic energy is $84 \%$ of total energy is

A body is executing SHM, if the force acting on the body is 6 N. When the displacement is 2 cm, then the force acting on the body at a displacement of 3 cm is

Three springs are connected to a mass $m$. When mass $m$ oscillates, what is the effective spring constant and time period of vibration? Given $k=2 \mathrm{~Nm}^{-1}$ and $m=80 \mathrm{~g}$.

To make the frequency of an oscillator double, one has to

If a spring of mass $30 \mathrm{~kg}$ has spring constant of $15 \mathrm{~N} / \mathrm{m}$, then its time period, is

Statement-I: If Amplitude of SHM is doubled, the periodicity wall remain same.

Statement-II: Amlitude and periodicity are two independent characteristics of SHM.

A pendulum made of a uniform wire of cross – sectional area A has time period T. When an additional mass M is added to its bob, the time period changes ${T_M}.$ If the Young’s modulus of the material of the wire is Y, then $\frac{1}{Y}$ is equal to ( $g$ = gravitational acceleration)

A particle is executing SHM of period 24 $x$ and of amplitude 41 cm with O as equilibrium position. The minimum time in seconds taken by the particle to go from P to Q. where OP = -9 cm and OQ =40 cm 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

Which one of the following statements is
correct?

At a given instant of time the position vector of a particle moving in a circle with a velocity $3 \hat{i}-4 \hat{j}+5 \hat{k}$ is $\hat{i}+9 \hat{j}-8 \hat{k}$. Its angular velocity at that time is

When a simple pendulum is moved from the Earth's surface to deep mine, the period of oscillation