An object of mass m is attached to a spring. The restoring force of the spring is F = − λ x 3 , where x is the displacement. The oscillation period depends on the mass, λ and oscillation amplitude. Su

Question

An object of mass m is attached to a spring. The restoring force of the spring is F = − λ x 3 , where x is the displacement. The oscillation period depends on the mass, λ and oscillation amplitude. Suppose the object is initially at rest. If the initial displacement is D then its period is τ . If the initial displacement is 2D, find the period. (Hint: use dimension analysis.)

TestHub · Accepted Answer

[ λ ] = L 3 MLT − 2 ​ = ML − 2 T − 2 τ ∝ m a λ b D c M 0 L 0 T 1 = M a ( ML − 2 T − 2 ) b L c M 0 L 0 T 1 = M a + b L − 2 b + c T − 2 b a + b = 0 − 2 b + c = 0 2 b = c − 2 b = 1 b = − 2 1 ​ c = − 1

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