(Solved): A chassis dynamometer is used to study the unsprung mass of an automobile as illustrated in Figure ...

A chassis dynamometer is used to study the unsprung mass of an automobile as illustrated in Figure P3.14, and discussed in Example 1.4.1. Compute the maximum magnitude of the center of the wheel due to an impulse of $5000\mathrm{N}$ applied over 0.01 seconds in the $x$ direction. Assume the wheel mass is $m=15\mathrm{kg}$, the spring stiffness is $k=500,000\mathrm{N}/\mathrm{m}$, the shock absorber provides a damping ratio of $?=0.3$, and the rotational inertia is $J=2.323\mathrm{kg}{\mathrm{m}}^2$. Assume that the dynamometer is controlled such that $x=r?$. Compute and plot the response of the wheel system to an impulse of $5000\mathrm{N}$ over $0.01\mathrm{s}$. Compare the undamped maximum amplitude to that of the maximum amplitude of the damped system (use $r=0.457\mathrm{m}$ ).