Question

A 46.5 kg block sits at rest on a frictionless, horizontal surface. It is connected horizontally, via a massless, ideal spring to a stationary wall. A force is then used to displace and hold the block in a new position (so that the spring is compressed). Then the block is released to move freely. In that first instant of motion, its acceleration is 7.98 m/s^2, and when it passes through its original (first) position, its speed is 13.2 m/s. What is the springs constant, k?

Answer 1

Maximum acceleration is w^2 A, where A is the amplitude, and w is the angular frequency of motion, 2 pi f.
The maximum velocity is wA.
Note that the ratio of maximum acceleration to maximum velocity, both of which you know, equals w.

Compute w and use the relation
w = sqrt(k/m) to determine k.