Oscillations

Consider a spring-mass simple harmonic oscillator in one dimension. The mass of the particle is $m \mathrm{~kg}$ and the spring constant is $k \mathrm{Nm}^{-1}$. At a given instant, the extension of the spring is $x$-meter and the speed of ...

A cylindrical cork of uniform density floats in a liquid of density $\rho_1$. If the cork is depressed slightly and released, it oscillates harmonically with time period $T$. If the same cork floats in another liquid of density $\rho_2$, th...

For a simple pendulum, having time period $T$, the variation of kinetic energy (K.E.) with time $(t)$ is represented by:

Savitha, a XI standard student, while conducting an experiment to determine the effective length of a simple pendulum $L$, notes down the data of time taken to complete 30 oscillations as 60 s and hence calculates the length of the simple p...

The sum of kinetic energy and potential energy of a simple pendulum bob is 0.02 joule. The speed of the simple pendulum bob at equilibrium position is approximately:
(Consider mass of the bob $=20 \mathrm{~g}$ )

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency $\omega(t)$ and average amplitude $A(t)$ of the system c...

Two identical point masses $P$ and $Q$, suspended from two separate massless springs of spring constants $k_1$ and $k_2$, respectively, oscillate vertically. If their maximum speeds are the same, the ratio ( $A Q / A_\rho$ ) of the amplitud...

The two-dimensional motion of a particle, described by \(\vec{r}=(\hat{i}+2 \hat{j}) A \cos \omega t\) is a/an:
A. parabolic path
B. elliptical path
C. periodic motion
D. simple harmonic motion
Choose the correct answer from the options giv...

A particle executing simple harmonic motion with amplitude A has the same potential and kinetic energies at the displacement

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is \(\frac{x}{2}\) times its original time period. Then the value ...

If \(x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}\) represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are

A simple pendulum oscillating in air has a period of \(\sqrt{3} \mathrm{~s}\). If it is completely immersed in non-viscous liquid, having density \(\left(\frac{1}{4}\right)^{\text {th }}\) of the material of the bob, the new period will be ...

The \(x\) - \(t\) graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at \(t=2 \mathrm{~s}\) is :

Identify the function which represents a non-periodic motion.

Match List-I with List-II

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Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at th...

A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is -

A body is executing simple harmonic motion with frequency 'n', the frequency of its potential energy is :

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is :

The displacement of a particle executing simple harmonic motion is given by
y = A0 + A sin\(\omega\)t + B cos\(\omega\)t.
Then the amplitude of its oscillation is given by :

The radius of circle, the period of revolution, initial position and sense of revolution are indicated is the figure.

y- projection of the radius vector of rotating particle P is :

Average velocity of a particle executing SHM in one complete vibration is :

A pendulum is hung from the roof of a
sufficiently high building and is moving freely
to and fro like a simple harmonic oscillator.
The acceleration of the bob of the pendulum
is 20 m s–2 at a distance of 5 m from the mean
position. The tim...

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is

A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is K'. Then they are connected in parallel and force constant is k''. Then k' : k'' is

A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased b...

When two displacements represented by y1 = a sin\({\left( {\omega t} \right)}\) and y2 = b cos\({\left( {\omega t} \right)}\) aresuperimposed the motion is

A particle is executing SHM along a straight line. Its velocities at distances x1 and x2 from the mean position are V1 and V2 respectively. Its time period is

A particle is executing a simple harmonic motion. Its maximum acceleration is \(\alpha\) and maximum velocity is \(\beta\). Them, its time period of vibration will be

The oscillation of a body on a smooth horizontal surface is represented by the equation,
X = A cos\(\left( {\omega t} \right)\)
where X = displacement at time t
\(\omega\) = frequency of oscillation
Which one of the following graphs show...

A particle of mass m oscillates along x-axis according to equation x = asin\(\omega\)t. The nature of the graph between momentum and displacement of the particle is

Out of the following functions representing motion of a particle which represents SHM
(1)  y = sin\(\omega\)t \(-\) cos\(\omega\)t
(2)  y = sin3\(\omega\)t
(3)  y = 5cos\(\left( {{{3\pi } \over 4} - 3\omega t} \right)\)
(4)  y = 1 + $$\o...

Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean posit...

The period of oscillation of a mass M suspended from a strong of negligible mass is T. If along with it another mass M is also suspended, the period of oscillation will now be

The displacement of a particle along the x-axis is given by x = asin2\(\omega\)t. The motion of the particle corresponds to

A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The speed of the pendulum at x = a/2 will be

Which one of the following equations of motion represents simple harmonic motion ?
where k, k0, k1 and a are all positive.

Two simple harmonic motions of angular frequency 100 and 1000 rad s\(-\)1 have the same displacement amplitude. The ratio of their maximum acceleration is

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

A particle executes simple harmonic oscillation with an amplitude \(a\). The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

The particle executing simple harmonic motion has a kinetic energy K0cos2\(\omega\)t. The maximum values of the potential energy and the total energy are respectively

A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible.
When pressed slightly and released the mass executes a simple harmonic motion...

A rectangular block of mass m and area of cross-section A floats in a liquid of density \(\rho\). If it is given a small vertical displacement from equilibrium it undergoes with a time period T, then

The circular motion of a particle with constant speed is

Two springs of spring constants k1 and k2 are joined in series. The effective spring constant of the combination is given by

A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is

The potential energy of a simple harmonic oscillator when the particle is half way to its end point is

In case of a forced vibration, the resonance peak becomes very sharp when the

Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion?

The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be