Chapter 11.4, Problem 6E

(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 $z=\cosh x$. 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 $z_{\max }=\frac{2g\cosh \left(x_0\right)}{2g-{\nu }_0^2\cosh \left(x_0\right)}$.