Chapter 6.4, Problem 56PE

In a course in differential equations or physics, a more specific model for a mass moving in damped harmonic motion is found as $d=a{e}^{-be/\left(2m\right)}\cos \left(t\sqrt{{\omega }^2-{\left(\frac{b}{2m}\right)}^2}\right)$ where $b$ is a damping constant unique to the 0physical system $m$ is the mass of the object, and |a| is the displacement at time $t=0$ . The value $\frac{2\pi }{\omega }$ is the related period under simple harmonic motion. Use this model for Exercises 55-56.

a. Write a model for damped harmonic motion for the bob of a pendulum of mass of $2\text{ kg}$ originally pulled to the right of its equilibrium position $0.6\text{ m}$ . Upon release, the bob makes

one complete swing back and forth in $2\sec$ with a damping constant $b=0.2\frac{\text{N-s}}{\text{m}}$ .

b. Graph the model from part (a) on the window $\left[0,10,1\right]\text{ by }\left[-0.8,0.8,0.1\right].$