Superposition of SHMs – Rankers Physics
Topic: Oscillation
Subtopic: Equation of SHM

Superposition of SHMs

Assertion (A): A particle, simultaneously subjected to two simple harmonic motions of same frequency and same amplitude, will perform SHM only if the two SHM’s are in the same direction.
Reason (R): A particle, simultaneously subjected to two simple harmonic motions of same frequency and same amplitude, perpendicular to each other the particle can be in uniform circular motion.
 
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:

Assertion (A) is true: Superposition of parallel SHMs results in SHM. Assertion (R) is true: Perpendicular SHMs of same frequency and amplitude with \(frac{pi}{2}\) phase difference result in UCM. However, (R) explains a scenario where SHM is not formed along a line, not why (A) is true.

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