# 10.5 Applications of the Trigonometric Graphs

**Simple Harmonic Motion • Alternating Electric Current • Frequency**

When an object moves in a circular path with constant velocity (see Section 8.4), its *projection* on a diameter moves with **simple harmonic motion.** For example, the shadow of a ball at the end of a string and moving at a constant rate, moves with simple harmonic motion. We now consider this physical concept and some of its applications.

# Example 1 Simple harmonic motion

In Fig. 10.33, assume that a particle starts at the end of the radius at (`R`, 0) and moves counterclockwise around the circle with constant angular velocity $\omega \hspace{0.17em}.\hspace{0.17em}$ *The displacement of the projection on the y-axis is d* and is given by $d\hspace{0.17em}=\hspace{0.17em}R\mathrm{sin}\text{}\theta \hspace{0.17em}.\hspace{0.17em}$ The displacement is shown ...

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