A certain mass-spring-damper system has the following equation of motion: 40 + c + 1200x = f(t), where r(t) represents the displacement of the mass. The initial conditions are zero and the applied force on this system is a step function of magnitude 6000 N. For this given data,
a) Solve for r(t) with damping coefficient values of 680 Ns/m and 200 Ns/m manually and using MATLAB (Show all your steps for the manual procedure. You will get a zero if you don't show your steps)
b) Plot the response resulting from two values of damping coefficients using MATLAB in a single plot. You are expected to clearly label the axis, differentiate the curves using different linetypes, and add a legend to differentiate the curves resulting from two values of damping coefficients.
c) Using your algebraic expressions of the solution for the two damping coefficients, find expressions for the velocity of the mass. Plot the velocity of the mass for the two values of damping coefficients using MATLAB in a single plot. You are expected to clearly label the axis, differentiate the curves using different linetypes, and add a legend to differentiate the curves resulting from two values of damping coefficients.
d) Instead of a step function, if the forcing function has a magnitude 1000 N and turns on and off in repeated intervals of 60 seconds, sketch the input and system responses using MATLAB in a single plot. You are expected to clearly label the axis, differentiate the curves using different linetypes, and add a legend to differentiate the curves resulting from two values of damping coefficients. Your plots should extend for a reasonable duration.
