Elasticity & SHM — JEE Main PYQs

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire-2 has cross-sectional area 3A. If the length of wire 1 increases by $\Delta x$ on applying force F, how much force is needed to stretch wire 2 by the same amount?

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=2\times 10^{-2}\cos \pi t$ metres. The time at which the maximum speed first occurs is

Two springs, of force constants $k_1$ and $k_2$, are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$. If both ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are made four times their original values, the frequency of oscillation becomes

A particle of mass $m$ executes simple harmonic motion with amplitude 'a' and frequency 'v'. The average kinetic energy during its motion from the position of equilibrium to the end 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

Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy?

The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is $4.4\mathrm{m}/\mathrm{s}$. The period of oscillation is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega$. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

A wire elongates by $\ell \mathrm{mm}$ when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm)

A particle of mass 0.3 kg is subjected to a force $\mathrm{F}=-\mathrm{kx}$ with $\mathrm{k}=15\mathrm{N}/\mathrm{m}$. What will be its initial acceleration if it is released from a point 20 cm away from the origin?

If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

The function ${\sin }^2(\omega t)$ represents

Two simple harmonic motions are represented by the equation $y_1=0.1\sin \left(100\pi t+\frac{\pi }{3}\right)$ and $y_2=0.1\cos \pi t$. The phase difference of the velocity of particle 1 w.r.t. the velocity of the particle 2 is

If a simple harmonic motion is represented by $\frac{d^{2}x}{d{t}^2}+\alpha x=0$, its time period is

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

A wire fixed at the upper end stretches by length by applying a force $F$. The work done in stretching is

The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is $t_0$ in air. Neglecting frictional force of water and given that the density of the bob is …

A particle at the end of a spring executes simple harmonic motion with a period $t_1$, while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $t$, then

The total energy of particle, executing simple harmonic motion is

A particle of mass $m$ is attached to a spring (of spring constant $k$) and has a natural angular frequency ${\omega }_0$. An external force $F(t)$ proportional to $\cos \omega t$ ($\omega \ne {\omega }_0$) is applied to the oscillator. The time displacement of the oscillator will …

In forced oscillation of a particle the amplitude is maximum for a frequency ${\omega }_1$ of the force, while the energy is maximum for a frequency ${\omega }_2$ of the force, then