Question

Hooke's law says that the return force for a spring operating in its linear region is proportional to the displacement from its equilibrium length (F=-kx). If a block is attached to such a spring, pulled/pushed from equilibrium (x=0) and allowed to slide back and forth (frictionlessly), it will undergo simple harmonic motion. That is, its displacement will be of the form x(t)= x(sub0)cos(2pi t/T) where A is the initial displacement, t is the time, and T is the period. Using the relationship between position, velocity, and acceleration together with Newton's Second law (F=ma)