Oscillations

JEE Main 2025 (Online) 23rd January Morning ShiftMCQMedium📈 Topic in 5% papers+4−1

Ques. 1JEE Main 2025, 23 January (Morning Shift)

A light hollow cube of side length 10 cm and mass 10 g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is y 10-2 s, where the value of y is (Acceleration due to gravity, g=10 m/s2, density of water =103 kg/m3 )

Answer

(1) 2

Solution

Pushed down by x, the extra upthrust is the restoring force: F=- Ag x, so k= Ag (SHM).

[figure]

k=103 10-2 10=100 N m-1, m=10-2 kg

T=2 mk=2 10-2 s y=2

Answer: (1)

Keep practising — Oscillations

Ques. 2JEE Main 2025, 22 January (Evening Shift)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the correct answer from the options given below :

Both (A) and (R) are true and (R) is the correct explanation of (A)
(A) is false but (R) is true
(A) is true but (R) is false
Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

Ques. 3JEE Main 2024, 9 April (Morning Shift)

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m, 2 ms-1 and 16 ms-2 at a certain instant. The amplitude of the motion is x m where x is .

Ques. 4JEE Main 2024, 9 April (Evening Shift)

A particle of mass 0.50 kg executes simple harmonic motion under force F = -50( Nm-1)x. The time period of oscillation is x35 s. The value of x is . (Given = 227)

Ques. 5JEE Main 2024, 8 April (Evening Shift)

An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of ( 25 )Hz. At the position x = 0.04 m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is cm.

Ques. 6JEE Main 2024, 6 April (Morning Shift)

A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is cm/s.

Ques. 7JEE Main 2024, 4 April (Evening Shift)

In simple harmonic motion, the total mechanical energy of given system is E. If mass of oscillating particle P is doubled then the new energy of the system for same amplitude is: [figure]

E/ 2
2E
E 2
E

Ques. 8JEE Main 2024, 4 April (Evening Shift)

The displacement of a particle executing SHM is given by x = 10 ( t + 3 ) m. The time period of motion is 3.14 s. The velocity of the particle at t = 0 is m/s.

Ques. 9JEE Main 2024, 1 February (Evening Shift)

A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency f1. The frequency of oscillations if a mass 9 m is suspended from the same spring is f2. The value of f1f2 is .

Ques. 10JEE Main 2024, 31 January (Morning Shift)

A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is 2A3. The new amplitude of motion is nA3. The value of n is .

Ques. 11JEE Main 2024, 31 January (Evening Shift)

The time period of simple harmonic motion of mass M in the given figure is M5k, where the value of is . [figure]

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