SHM of two particles – Rankers Physics
Topic: Oscillation
Subtopic: Angular SHM and Simple Pendulum

SHM of two particles

Assertion (A): Two particles are in SHM with same time period, same amplitude, same position and same speed are in the same phase.
Reason (R): Phase of particle depends on position and speed of particle.
 
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:

The position of a particle in SHM is given by \(x = A cos(omega t + phi)\) and velocity by \(v = -Aomega sin(omega t + phi)\). Given same amplitude \(A\), time period \(T\) (thus \(omega\)), position \(x\), and speed \(v\), the phase \(phi\) must be the same. Thus, A and R are true and R is the correct explanation of A.

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