Simple Harmonic Motion - Mechanics - Physics Previous Year Questions

A simple pendulum consists of a small sphere of mass $m$ suspended by a thread of length $l$. The sphere carries a positive charge $q$. The pendulum is allowed to do small oscillations in uniform electric field $E$ with direction vertically upwards. The time period of oscillation is

A body starting at $t=0$ from origin oscillates simple harmonically with a period of 4 s . After what time will its kinetic energy by $75 \%$ of its total energy?

A clock is designed based on the oscillation of a spring-block system suspended vertically in the absence of air-resistance. Assume it shows the correct time when a spring of stiffness $k$ and block is mass $m$ are used. If the block is replaced by another block of mass $4 m$, choose the correct option

A force of 6.4 N stretches a vertical spring by 0.1 m . If it were to oscillate with a period of $\pi / 4$, then the mass that is to be suspended from the spring is

A pendulum has a time period $T$ in air. Whạt it is made to oscillate in water its time period is $\sqrt{2} T$. Then the relative density of the material of the bob of the pendulum is (neglect damping)

The displacement of a particle is given by the relation $x=4(\cos \pi t+\sin \pi t)$. The amplitude of the particle is

The displacement of a particle executing simple harmonic motion is given by $x=2 \cos (t)$ where $t$ is the time in seconds then the time period of the particle is

A point mass oscillates along the $X$-axis according to the law $x=x_0 \cos \left(\omega t-\frac{\pi}{4}\right)$. If the acceleration of the particle is written as $a=A \cos (\omega t-\delta)$, then

For a particle executing SHM, determine the ratio of average acceleration of the particle between extreme position and equilibrium position w.r.t. the maximum acceleration.

The amplitude of a damped oscillator varies with time as $A(t)=A_0 \exp (-b t / 2 \mathrm{~m})$, where $b=70 \mathrm{~g} / \mathrm{s}$ and $m=200$ g. How long does it take for the mechanical energy to drop to one-fourth of its initial value?

[Take, $\ln 2=0.7$ ]

A simple pendulum of length 1 m and having a bob of mass 100 g is suspended in a car, moving on a circular track of radius 100 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, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

A block is in simple harmonic motion (SHM) on the end of the spring with position given by $x=5 \cos \left(\omega t+\frac{\pi}{4}\right) \mathrm{cm}$. If the total mechanical energy used is 100 J to achieve maximum displacement, then the potential energy at time, $t=0$ is

A particle performs simple harmonic motion with a time period of 16 s . At a time $t=2 \mathrm{~s}$, the particle passes through the origin and at $t=4 \mathrm{~s}$ its velocity is $4 \mathrm{~m} / \mathrm{s}$. The amplitude of the motion is

A stiff spring having spring constant $k=400 \mathrm{~N} / \mathrm{m}$ is attached to the floor vertically. A mass $m=10 \mathrm{~kg}$ is placed on top of the spring. The block oscillates if it is pressed downward and released. Find the extension in the spring at which the block loses contact with spring. (Take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

Consider a simple harmonic motion (SHM). Let $K$ and $U$ be kinetic energy and potential energy when the displacement in SHM is one-half $\left(\frac{1}{2}\right)$ the amplitude.

Which of the correct statement?

A particle is exhibiting simple harmonic motion has its displacement $x$ and velocity $v$ related as $4 v^2=25-x^2$. The time period of SHM is

Three masses $700 \mathrm{~g}, 500 \mathrm{~g}$ and 400 g are suspended at the end of a spring shown in figure and are in equilibrium. When the 700 g mass is removed, the system oscillates with a time period of 3 s . If 500 g mass is further removed, then it will oscillate with a period of

A particle is executing simple harmonic motion in one-dimension. If the amplitude of oscillations is 0.2 cm and if its velocity at the mean position is $5 \mathrm{~m} / \mathrm{s}$, then the angular frequency of the oscillation is

A body is oscillating in simple harmonic motion according to the equation $x=6 \cos \left(2 \pi t+\frac{\pi}{3}\right) \mathrm{m}$. The magnitude of the acceleration (in $\mathrm{m} / \mathrm{s}^2$ ) of the body at $t=\mathrm{ls}$