Chapter 10.4, Problem 5E

(a)

To determine

To show: The solution is periodic by the phase plane method if the system is undamped such that the bead is released from the position $x\left(0\right)=x_0$ and the shape function of the wire is $z=\frac{x^2}{2}$. The initial velocity of the bead is $x^{\prime }\left(0\right)={\nu }_0$ centimeter per second.

(b)

To determine

To show: The maximum height $z_{\max }$ attained by the bead is $z_{\max }=\frac{1}{2}\left(e^{\left(\frac{{\nu }_0^2}{g}\right)}\left(1+x_0^2\right)-1\right)$.