Consider the spring-mass system shown. A mass of m = 5kg has stretched a spring by s_0 = 1.5 meters and is at rest. A damping system is connected that provides a damping force equal to 30 times the instantaneous velocity of the mass. At time t=0, the mass at rest has an external force of f(t) = 25sin(10t) applied. Please write a differential equatioin that models the mass location y(t) as a function of time.

Consider the spring-mass system shown. A mass of m = 5kg has stretched a spring by s_0 = 1.5 meters and is at rest. A damping system is connected that provides a damping force equal to 30 times the instantaneous velocity of the mass. At time t=0, the mass at rest has an external force of f(t) = 25sin(10t) applied. Please write a differential equatioin that models the mass location y(t) as a function of time.

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