In SHM, the general equations for position, velocity, and acceleration are:

x(t) = A cos(ωt + δ)

v = dx/dt = -Aω sin(ωt + δ)

a = d²x/dt² = -Aω² cos(ωt + δ)

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

x_max = A

v_max = Aω

a_max = Aω²

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.

Comparing the mass on the spring (SHM system) to the object undergoing uniform circular motion, not only do the x positions match, but the mass' velocity matches the x-component of the circular motion velocity, and the mass' acceleration matches the x-component of the circular motion acceleration.