16.6 Uniform Circular Motion and Simple Harmonic Motion

Some modules occasionally refer to the connection between uniform circular motion and simple harmonic motion. Moreover, if you carry your study of physics and its applications to greater depths, you will find this relationship useful. It can, for example, help to analyze how waves add when they are superimposed.

Identify an object that undergoes uniform circular motion. Describe how you could trace…

(a)What is the maximum velocity of an 85.0-kg person bouncing on a bathroom scale having a force constant of $1 . \text{50} \times \text{10}^{6} \text{N}/\text{m}$, if the amplitude of the bounce is 0.200 cm? (b)What is the maximum energy stored in the spring?

At what positions is the speed of a simple harmonic oscillator half its maximum? That is, what values of $x / X$ give $v = \pm v_{\text{max}} / 2$, where $X$ is the amplitude of the motion?