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 = 1 × 1 0 × 1 0 0 2 5 × 2 5 + 1.6   cm = 8 5 + 1.6 = 1.6 + 1.6 =  3.2 cm ∴   F m a x = 4 g   +   K ( x   +   A )     =   40   +   20   =   60   N