To understand the application of the general harmonic equation to the kinematics of a spring oscillator.
One end of a spring with spring constant is attached to the wall. The other end is attached to a block of mass . The block rests on a frictionless horizontal surface. The equilibrium position of the left side of the block is defined to be . The length of the relaxed spring is . (Intro 1 figure)
The block is slowly pulled from its equilibrium position to some position along the x axis. At time , the block is released with zero initial velocity.
The goal is to determine the position of the block as a function of time in terms of and .
It is known that a general solution for the displacement from equilibrium of a harmonic oscillator is
where , , and are constants. (Intro 2 figure)
Your task, therefore, is to determine the values of and in terms of and .