Basic Technical Mathematics, 11th Edition

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 $d\hspace{0.17em}=\hspace{0.17em}R\sin \theta \hspace{0.17em}.\hspace{0.17em}$ The displacement is shown ...