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A force of 400N stretches a spring 2m. A mass of 50kg is attached to the...

A force of 400N stretches a spring 2m. A mass of 50kg is attached to the end of the spring and put in a viscous fluid with a damping force that is 100 times the instantaneous velocity. The mass is released from the equilibrium position with a downward velocity of 1m/s.

(a) Determine the natural frequency of the system.

(b) Determine the level of damping in the system.

(c) Write the differential equation of motion

(d) Solve the system and find the position of the mass at 5s.

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