A body is in simple harmonic motion with time period T = 0.5 s and amplitude A = 1 cm . Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

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∴ x = A sin ⁡ ω t A 2 = A sin ⁡ ω t ω t = π 6 t = π 6 ω = π 6 × 2π t = T 12 ∴ T i m e t a k e n t o r e a c h f r o m x = 0 t o x = A 2 i s T 12 ∴ A v e r a g e v e l o c i t y = D i s p l a c e m e n t T i m e = A / 2 T / 12 = A T × 6 = 6 × 1 0.5 = 12 c m / s

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