What Are the Key Factors in Solving Mechanical Vibration Problems?

[s7b]

Hi,

I don't understand how to go about solving a problem like this;

A weight stretches a spring 3 inches. It is set in motion at a point 4 inches below it's equilibrium point with zero velocity.

-Find the maximum amplitude
-When does it reach (the first time) it's highest point
-Find it's maximum velocity

 

[matematikawan]

Your governing equation will be
$$m\ddot{y} + ky = 0$$
which is a simple harmonic motion

Hi,
A weight stretches a spring 3 inches.

This will allowed you to compute k/m.

Hi,

It is set in motion at a point 4 inches below it's equilibrium point with zero velocity.

This is the initial condition which will allowed you to determined the arbitrary constants when solving the governing equation.