A small industrial washing machine with a mass of 30kg is mounted on a spring. The product design specification states that the machine must have an undamped natural frequency of 3Hz. A viscous damper system is also attached to the machine which resists the motion with a force proportional to velocity equal to 1.3kN when the velocity is 2m/s.

Find the

i) required stiffness of the spring in the machine

ii) damping ratio

iii) damped natural frequency

iv) damped time period

v) the equation of motion

State

If the machine is given an initial displacement of 20mm and then allowed to decay.

Calculate

vi) the displacement after 1 second.