Question: Suppose a mass spring system is given by the ODE (12 points ) Suppose a mass spring system is given by the ODE 2xx+ cx'

Suppose a mass spring system is given by the ODE

(12 points ) Suppose a mass spring system is given by the ODE 2xx"+ cx' + 872x =0 a. Identify the values of c 2 0 for which the system is . Overdamped . Critically damped . Underdamped b. Pick your favourite value of c > 0 (note you cannot use c = 0) which is underdamped. Write down a general solution of the system. c. Now suppose c = 0 but there is an external force which is given by the periodic extension of F(t) = 4t for - 1

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