In SHM (simple harmonic motion), the general equations for position, velocity, and acceleration are:

x(t) = A cos(wt + q_o)

v(t)	= -Aw sin(wt + qo)

a(t)	= -Aw2 cos(wt + qo)

The phase angle q_o is determined by the initial position and initial velocity.

The angular frequency is determined by the system. For an object of mass m oscillating on a spring of spring constant k the angular frequency is given by:

w2

=

k m

Whatever is multiplying the sine or cosine represents the maximum value of the quantity. Thus:

x_max = A

v_max = Aw

a_max = Aw²

Graphing the position, velocity, and acceleration allows us to see some of the general features of simple harmonic motion:

• The speed is maximum when the object passes through the equilibrium position (x = 0)
• The acceleration is opposite in direction, and proportional to, the displacement
• All three graphs have the same frequency - they just differ by phases of 90 degrees.

The first set of graphs is for an angular frequency w = 1 rad/s. The second set of graphs is for w = 0.6 rad/s. This change of w is accomplished either by decreasing the spring constant or by increasing the mass. Which change did we make in this case?

1. We decreased the spring constant
2. We increased the mass
3. We could have done one or the other, you can't tell the difference