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 ω .  The displacement of the projection on the y-axis is d and is given by d = Rsin θ .  The displacement is shown ...

Get Basic Technical Mathematics, 11th Edition now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.