Using the general equation for x(t) given in the problem introduction, express the initial position of the block in terms of C,S,and omega .

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 .

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 .

## This question was asked on May 04, 2010.

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