$3\mathrm{.}19$ A $150$ pound boy stands at the edge of the diving board of Problem $2\mathrm{.}30,$ preparing to execute a dive. During this time, he shifts his weight in a leaping motion, moving up and down at the rate of $1$ cps $.$ If$,$ at the apogee of each bob his feet just touch the board so that they are nearly losing contact, determine the steady state motion of the boy.

Use information from problem $2\mathrm{.}30$ in Homework Assignment $03$

$3\mathrm{.}20$ A controller is attached to the pendulum of Problem $3\mathrm{.}5.$ If a sensor measures the amplitude of the motion of the pendulum driven by the applied force to be $\backslash ($ X$\_\{1\}\backslash ),$ determine the moment that must be exerted by the actuator to maintain the quiescence of the system.

Please solve both questions