As shown in the figure, the spring is unstretched when a man begins pulling on the cord. The mass of the block is M . Provided the man exerts a constant force F , determine the amplitude and the time period of the block's motion.

Step-by-step solution

Let x be the displacement of the block from its initial unstretched position. The equation of motion for the block is given by: M x = F - kx This can be rewritten as: M x = -k (x - F k ) This equation represents Simple Harmonic Motion (SHM) with a shifted equilibrium position. The new equilibrium position is where the net force is zero, i.e., x₀ = F k . Since the block starts from rest at the unstretched position ( x = 0 ), this initial position is one of the extreme positions of the SHM. The amplitude A of the mot