Exercise $4\mathrm{.}3\mathrm{.}5$

Ode $(4\mathrm{.}53)46$ u$\text{'}\text{'}+1700$u$\text{'}+15,000$u$=-450\mathrm{.}8$

Please do a and b

$($a$)$ Redo the solution for the ODE $(4\mathrm{.}53)$ in the bike shock absorber Example $4\mathrm{.}20,$ but change the damping constant from $c=1700$ to $c={10}^4,$ so the system is heavily overdamped. Plot the solution and redo Reading Exercise $4\mathrm{.}3\mathrm{.}3$ with this parameters. What disadvantage might such a value of $c$ have for the rider?

$($b$)$ Redo the solution for the ODE $(4\mathrm{.}53)$ in the bike shock absorber Example $4\mathrm{.}20$ but change the damping constant from $c=1700$ to $c=1200.$ Show that the system is now underdamped. Plot the solution and redo Reading Exercise $4\mathrm{.}3\mathrm{.}3.$ What disadvantage might an underdamped system have for the rider?