Question: 2. The figure below illustrates a mass that is connected to a movable base via a spring and a damper. The positions of the

2. The figure below illustrates a mass that is connected to a movable base via a spring and a damper. The positions of the mass and base are defined by x and xb, respectively. Assume that the mass and the base are initially motionless with the spring connection undeflected. The base is given the constant acceleration of x = g/5. (a) Derive the equation of motion. (b) Find the homogeneous and particular solutions. Find also the complete solution satisfying the initial conditions. (c) For mg = 300 lb (g = 386.4 in/s), k = 776 lb/in, c = 24.4 lb s/in, plot the mass's motion for two periods of damped oscillations. Submit Matlab or Python code (m or py file). 00 x Uncompressed/ Unstretched Spring Position Xb k w m Figure 2: Mass with movable base.

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