Oscillations

14 JEE Main questions · Physics

Oscillating systems

PhysicsJEE Main 22 Jan 2026, Shift 2·Q2·MCQ·Easy–moderate
Open
Using a simple pendulum experiment g is determined by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L and time period T ?
1. (1)
2. (2)
3. (3)
4. (4)
PhysicsJEE Main 23 Jan 2026, Shift 1·Q6·MCQ·Easy–moderate
Open
A simple pendulum of string length 30 cm performs 20 oscillations in 10s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is cm. [Assume that the mass of the pendulum remains same.]
1. (1)120
2. (2)0.75
3. (3)7.5
4. (4)15
PhysicsJEE Main 24 Jan 2026, Shift 1·Q3·MCQ·Easy–moderate
Open
A cylindrical block of mass $M$ and area of cross section $A$ is floating in a liquid of density $\rho$ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is .
1. (1) $2\pi\sqrt{\dfrac{M}{\rho A g}}$
2. (2) $\pi\sqrt{\dfrac{2M}{\rho A g}}$
3. (3) $\pi\sqrt{\dfrac{\rho A}{M g}}$
4. (4) $2\pi\sqrt{\dfrac{\rho A}{M g}}$
PhysicsJEE Main 24 Jan 2026, Shift 1·Q11·MCQ·Easy–moderate
Open
A spring of force constant 15 N/m is cut into two pieces. If the ratio of their length is $1:3$ , then the force constant of smaller piece is N/m
1. (1)15
2. (2)20
3. (3)60
4. (4)45
PhysicsJEE Main 28 Jan 2026, Shift 2·Q17·MCQ·Easy–moderate
Open
As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is:
1. (1)30
2. (2)27
3. (3)20
4. (4)5
PhysicsJEE Main 4 Apr 2026, Shift 2·Q10·MCQ·Moderate
Open
A uniform disc of radius $R$ and mass $M$ is free to oscillate about the axis A as shown in the figure. For small oscillations the time period is . ( $g$ is acceleration due to gravity)
1. (1) $2\pi\sqrt{\dfrac{5R}{4g}}$
2. (2) $2\pi\sqrt{\dfrac{2R}{3g}}$
3. (3) $2\pi\sqrt{\dfrac{3R}{2g}}$
4. (4) $2\pi\sqrt{\dfrac{3R}{g}}$
PhysicsJEE Main 6 Apr 2026, Shift 2·Q11·MCQ·Moderate
Open
A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maximum energy in the spring are Hz and J, respectively. (Take $g = 10\ \mathrm{m/s^2}$ )
1. (1) $\dfrac{5\sqrt{50}}{\pi}$ and $8\times10^{-3}$
2. (2) $\dfrac{5\sqrt{50}}{\pi}$ and 8
3. (3) $10\sqrt{50}$ and $2\times10^{-3}$
4. (4) $\dfrac{5\sqrt{50}}{\pi}$ and $16\times10^{-3}$
PhysicsJEE Main 8 Apr 2026, Shift 2·Q12·MCQ·Easy–moderate
Open
The frequency of oscillation of a mass $m$ suspended by spring is $\nu_1$ . If the length of the spring is cut to half, the same mass oscillates with frequency $\nu_2$ . The value of $\dfrac{\nu_2}{\nu_1}$ is .
1. (1)1
2. (2)2
3. (3) $\sqrt2$
4. (4) $\sqrt3$
We corrected a printing error in the original paper
Source printed the frequencies with a Latin $v$ ( $v_1$ , $v_2$ ) for $\nu$ .

SHM basics

PhysicsJEE Main 21 Jan 2026, Shift 2·Q8·MCQ·Easy–moderate
Open
The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad/s. The frequency of this simple harmonic oscillator is Hz. $\left[\text{take } \pi = \dfrac{22}{7}\right]$
1. (1)14
2. (2)88
3. (3)28
4. (4)176
PhysicsJEE Main 28 Jan 2026, Shift 1·Q21·Numerical·Easy–moderate
Open
The displacement of a particle, executing simple harmonic motion with time period $T$ , is expressed as $x(t) = \mathrm{A}\sin\omega t$ , where $A$ is the amplitude. The maximum value of potential energy of this oscillator is found at $t = T/2\beta$ . The value of $\beta$ is .
PhysicsJEE Main 2 Apr 2026, Shift 2·Q20·MCQ·Easy–moderate
Open
The equation of motion of a particle is given by $x = a\sin\left(50t + \pi/3\right)$ cm. The particle will come to rest at time $t_1$ and it will have zero acceleration at time $t_2$ . The $t_1$ and $t_2$ respectively are .
1. (1) $\dfrac{\pi}{300}$ s, $\dfrac{\pi}{75}$ s
2. (2) $\dfrac{\pi}{75}$ s, $\dfrac{\pi}{300}$ s
3. (3) $\dfrac{\pi}{300}$ s, $\dfrac{\pi}{25}$ s
4. (4) $\dfrac{\pi}{50}$ s, $\dfrac{\pi}{100}$ s
PhysicsJEE Main 4 Apr 2026, Shift 1·Q23·Numerical·Easy–moderate
Open
The velocity of a particle executing simple harmonic motion along x-axis is described as $v^2 = 50 - x^2$ , where $x$ represents displacement. If the time period of motion is $\dfrac{\alpha}{7}$ s, the value of $\alpha$ is .
We corrected a printing error in the original paper
Source printed the period as “ $\dfrac{x}{7}$ s, the value of $x$ ” ( $x$ already denotes the displacement).

PhysicsJEE Main 5 Apr 2026, Shift 2·Q10·MCQ·Moderate

Match List-I with List-II.

List-I		List-II
A.	$\sin^2\omega t$	I.	Periodic with time period $T = \dfrac{\pi}{\omega}$ but not simple harmonic motion (SHM)
B.	$\sin^3(2\omega t)$	II.	Periodic with time period $T = \dfrac{2\pi}{\omega}$ but Not SHM
C.	$\sin(\omega t) + \cos(\pi\omega t)$	III.	periodic with time period $T = \dfrac{\pi}{\omega}$ and SHM
D.	$\cos\omega t + \cos 2\omega t$	IV.	Non-periodic

Choose the correct answer from the options given below.

(1)A-III, B-I, C-IV, D-II
(2)A-II, B-I, C-III, D-IV
(3)A-III, B-II, C-IV, D-I
(4)A-II, B-I, C-IV, D-III

PhysicsJEE Main 6 Apr 2026, Shift 1·Q12·MCQ·Easy–moderate
Open
A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. the time required by it to move from $x = A$ to $x = \dfrac{A}{\sqrt2}$ is sec.
1. (1)1/4
2. (2)5/4
3. (3)5/8
4. (4)3/8