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Consider a horizontal spring-mass vibration system without damping, where the mass is 2 kg, the spring...

Consider a horizontal spring-mass vibration system without damping, where the mass is 2 kg, the spring is 18 N/m, and the external force is a periodic force f(t) = 6sin(3t):

a) Write the differential equation modeling the motion of this spring-mass system

b) Solve the differential equation in (a). Show Work

c) If at the initial time t = 0, the mass is at position 2 m to the right of the equilibrium position and its velocity is 1 m/s moving towards the left, find a particular equation y(t) that describes the position of the mass at time t.

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