A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is U x = k x 3 , where k is a positive constant. If the amplitude of oscillation is a , then its tim

Question

A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is U x = k x 3 , where k is a positive constant. If the amplitude of oscillation is a , then its time period T is

TestHub · Accepted Answer

U = k x 3 ⇒ F = - d U d x = - 3 k x 2 Also, for SHM x = a s i n ω t and d 2 x d t 2 + ω 2 x = 0 ⇒ Acceleration a = d 2 x d t 2 = - ω 2 x ⇒ F = m a = m d 2 x d t 2 = - m ω 2 x From equation (i) and (ii) we get ω = 3 k x m ⇒ T = 2 π ω = 2 π m 3 k x = 2 π m 3 k a s i n ω t ⇒ T ∝ 1 a .

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