Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad s - 1 , and amplitude 1 . 6 cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g = 10 m s - 2 ).

Step-by-step solution

Given ω = 2 5 rad/s and A = 1.6 cm ∴    ω = k m = 2 5 ⇒ k = 25 2 Maximum compression in the spring = x o + A = mg k + A ∴   F m a x = 4 g   +   k ( x 0   +   A ) F m a x   = 4 g + k mg k + A     =   40   +   20   =   60   N