A particle of mass 250 g executes a simple harmonic motion under a periodic force F = ( – 25 x ) N . The particle attains a maximum speed of 4 m s - 1 during its oscillation. The amplitude of the motion is ______ cm .

Step-by-step solution

Given, force F = ( – 25 x )   N ⇒ 0 . 25 a = - 25 x ⇒ a = - 100 x Now comparing it with standard equation, a = - ω 2 x we get ω = 10 . Now, v m a x = ω A ⇒ ω A = 4 ⇒ A = 4 10 = 0 . 4   m ⇒ A = 40   cm .