The system shown has a natural frequency, fn, of 5Hz,

m-10kg, J.-5kg-m², r=0.10m, and r=-0.25m. If the mass

is displaced 0.01m to the right and released from rest, the

amplitude of the resulting free vibration reduces by 80%

in exactly 10 cycles. Gravity may be taken as being into

the page.

a) Determine the equation of motion in terms of the

motion of the mass x(t).

b)

Determine the value of the stiffness k.

c) Determine the value of the damping coefficient c.