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A particle is moving with SHN in a straight line. When the distance of the particle from mean position has values x1 and x2 the corresponding values of velocities are v1 and v2. Show that the time period of oscillation is given by:→

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If a = amplitude ; y = displacement; w = angular frequency 

V = Velocity, then 

V2 = w2 (a2 – y2

For first case. u12 = w2(a2 – x12) →1)

( ∵velocity = u1 Displacement = x1

For second case, u22 = w2 (a2 – x22) →2)

(velocity = u2 Displacement = x2)

Subtracting equation 2) from equation 1); 

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