A block of mass m is connected to two identical massless springs, each of spring constant k . In the first case, the two springs are connected in series. In the second case, they are connected in parallel. If the block is given the same amplitude of oscillation in both cases, what is the ratio of its maximum speed in the first case to its maximum speed in the second case?

Step-by-step solution

The maximum speed of a block in simple harmonic motion is given by v_ = A = A k_ eq m . In the first case, the springs are in series. The equivalent spring constant is k_ series = k k k + k = k 2 . In the second case, the springs are in parallel. The equivalent spring constant is k_ parallel = k + k = 2k . Since the amplitude A and mass m are the same in both cases, the maximum speed is directly proportional to k_ eq . Therefore, the ratio of the maximum speeds is: v_ series v_ parallel = k_ series k_ parallel = k/