Chapter 5.2, Problem 81PE

(a)

To determine

To calculate: A model of the form $x\left(t\right)=\frac{v_0}{\omega }\sin \left(\omega t\right)+x_0\cos \left(\omega t\right)$ to represent the horizontal motion of the spring by using the following information. Here, the object completes 1 cycle in 1 sec $\left(\omega =1\right)$ . The horizontal position $x\left(t\right)$ of the object is given by $x\left(t\right)=\frac{v_0}{\omega }\sin \left(\omega t\right)+x_0\cos \left(\omega t\right)$ . Initially, the object moves 3ft to the left of the equilibrium position and then, given a velocity of 4ft/sec to the right.

(b)

To determine

To calculate: The function, $x\left(t\right)=4\sin t-3\cos t$ , which is obtained in the part (a) in the form of $x\left(t\right)=k\sin \left(t+\alpha \right)$ .

(c)

To determine

To calculate: The maximum displacement of the object from its equilibrium position.