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ENGG952 Engineering Computing-Functions of Motion

The motion of a damped spring-mass system is descirbed by the following ordinary differnetial equation:
where x is displacement from equlibrium position (meter), t is time (second), m is the mass and equal 20 kg, c is the damping coefficient (N.sec/meter) . The dampping coefficient, c, takes on two values of 5 (under damped), 40 (critically damped. The spring constant k = 20 N/meter. The initial velocity is zero, and the intial displacement x = 1 meter.

(a) Transform the problem into a system of two first order initial value ODEs. The report must clearly provide the detailed derivation of the technique.
(b) Solve for motion of a spring-mass system using the 2 nd order RK Huen method over the ?t ?1.0 . You can calcualte the results
manually or by matlab or by excel.
(c) Plot the displacment verus time for two values of the damping coefficient on the same figure, and discuss the results. 

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