IIT JEE , AIEEE Forum - Physics , Mechanics

Conjurer

Without loss of generality

we can say this SHM is the spring block SHM.

And we know that total energy of a particle executing SHM is 1/2mw^2a^2

Total mechanical energy = KE + PE

So 1/2 mw^2a^2 = 1/2 w^2mx^2 + 1/2mu^2

and 1/2 mw^2a^2 = 1/2 w^2my^2 + 1/2 mv^2 ( because k=w^2m)

Dividing both equations:

w^2(y^2-x^2) = (u^2-v^2)

w^2 = (u^2 - v^2)/(y^2-x^2)

T= 2pi/w = 2 [(y²-x²)/(u²-v²)]^1/2

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