Oscillations PYQs - Last 10 Years

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

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
...

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