A block attached to a horizontal spring slides on a frictionless surface. When the block is displaced s meters from its equilibrium position, the spring exerts a restoring force that produces an acceleration a(s)=−4s (in m/s2). Initially, the block is released from rest at s=1m.
(1) Part 1: (a) Write a differential equation that relates the velocity v of the block to its position s.
(2) Part 2: (b) Solve the equation from part (a) to obtain v explicitly as a function of s for the outward motion (s decreasing toward 0).
(3) Part 3: (c) Using a second appropriate differential equation, derive an expression for the time t required for the block to move from s=1m to the equilibrium position s=0m.
(4) Part 4: (d) Determine the maximum speed attained by the block during its motion and state when (in terms of position) that speed occurs.