A particle is describing simple harmonic motion. If its velocities are v 1 and v 2 when the displacements from the mean position are y 1 and y 2 respectively, then its time period is

Question

A particle is describing simple harmonic motion. If its velocities are v 1 ​ and v 2 ​ when the displacements from the mean position are y 1 ​ and y 2 ​ respectively, then its time period is

TestHub · Accepted Answer

In simple harmonic motion, velocity v = ω A 2 − y 2 ​ Solving equations (i) and (ii), we get ​ v 2 2 ​ − v 1 2 ​ = ω 2 ( y 1 2 ​ − y 2 2 ​ ) ω = y 1 2 ​ − y 2 2 ​ v 2 2 ​ − v 1 2 ​ ​ ​ ​ ⇒ T = ω 2 π ​ = 2 π v 2 2 ​ − v 1 2 ​ y 1 2 ​ − y 2 2 ​ ​ ​

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