PLEASE dont copy from anywhere ANSWER PART C only

A block of mass $m$ is traveling to the right on a smooth horizontal surface with a speed of $v.$ A spring

of stiffness $k$ and damper with damping constant $c$ are attached between the block and a massless

support. The support then strikes a stationary wall, at which point the support sticks to the wall for

all subsequent time. The coordinate $x$ describes the motion of the block as measured from the

position of the block at the instant the support first contacts the wall.

a$)$ Derive the equation of motion for the block after the support sticks to the wall in terms of $x.$

b$)$ If $k=500\frac{N}{m}$ and $c=40N\frac{s}{m},$ determine the mass of the block if the system has a

damping ratio of $0\mathrm{.}10(10\%$ damping$)$ after sticking to the wall.

c$)$ If $v=50\frac{m}{s},$ determine the maximum force required to prevent the support from pulling

away from the wall after sticking by completing the following steps:

i$.$ Write out the solution, $x(t),$ for the equation of motion.

ii$.$ If you didn't already do so in part i $,$ apply the initial conditions and solve for C and S $.$

iii. Plot the solution and indicate on the plot the point in time at which the maximum

required force occurs. $($You$\text{'}$ll need to think about where the components of the system

are at each moment in time.$)$ Include the plot or a sketch of the plot in the solution you

submit.

iv$.$ Determine the $x-$value for the point in time you identified in part iii. $($You can either do

this by solving for the exact value or by just picking the point off your plot.$)$

v$.$ Use the value you found in part iv to determine the force. $($If you're stuck, try drawing

an FBD for that specific point in time.$)$