Damped Oscillation Parameters – Rankers Physics

Energy in SHM: Practice Problem & Solution

Assertion (A): The amplitude of damped oscillation depends on damping constants. Reason (R): The angular frequency for a damped oscillation depends on damping constant only.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Energy in SHM. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true. The amplitude decay in damped oscillation is governed by a term involving the damping constant. Reason (R) is false. The angular frequency of a damped oscillation \(omega' = sqrt{omega_0^2 - gamma^2}\) depends on both the natural frequency \(omega_0\) and the damping constant \(gamma\), not solely on \(gamma\).

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. A particle of mass 0.1 kg executes SHM under a force F = (–10x) Newton. Speed of particle at mean position is 6 m/s. Then amplitude of oscillations is :
2. A linear harmonic oscillator of force constant $2 \times 10^6 \text{ N/m}$ and amplitude $0.01 \text{ m}$ has a total mechanical energy of $160 \text{ J}$. Its (1996)
3. A particle is executing S.H.M., If its P.E. & K.E. is equal then the ratio of displacement & amplitude will be :
4. A seconds pendulum is mounted in a rocket. Its period of oscillation will decrease when rocket is: (1994)
5. Assertion (A): Amplitude of SHM \(x = 4sin^2\omega t + 2cos^2\omega t + 2sin\omega t cos\omega t\) is \(sqrt{2}\). Reason (R): Angular frequency of given equation is \(2\omega\).