Example: Equation of Motion

An object is undergoing simple harmonic motion. The displacement as a function of time is shown in the graph on the right.

Question:

Write down the expression for the equation of motion of this object.

Answer:

• At t=0, y=0. So we can use
  y = Asin($\omega$t)

• The amplitude A is 15 cm
• The period T is 0.8 s
• Therefore the frequency is

  \[ \rm \omega = \frac{2 \pi}{T} = 7.85 s^{-1} \]

• So the equation of motion is:
  y = 15 sin(7.85 s^-1 t) cm.