Question

Learning Goal:

To understand the application of the general harmonic equation to finding the acceleration of a spring oscillator as a function of time. One end of a spring with spring constant k is attached to the wall. The other end is attached to a block of mass m. The block rests on a frictionless horizontal surface. The equilibrium position of the left side of the block is defined to be x=0. The length of the relaxed spring is L.

The block is slowly pulled from its equilibrium position to some position xinit>0 along the x axis. At time t=0 , the block is released with zero initial velocity. The goal of this problem is to determine the acceleration of the block a(t) as a function of time in terms of k, m, and xinit. It is known that a general solution for the position of a harmonic oscillator is x(t)=Ccos(?t)+Ssin(?t), where C, S, and ? are constants.

Using the relation between acceleration and position, find the acceleration of the block a(t)a(t) as a function of time.

Express your answer in terms of ωω, tt, and x(t)x(t).

Answer 1