Problem (60 marks]: The following differential equation represents a mass-spring- damper system as shown. XIE к -Elt) m

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Problem (60 marks]: The following differential equation represents a mass-spring- damper system as shown. XIE к -Elt) m mä +ci+kx = 10 sin(210ft), where: m = 2.3 kg c = 10 N.s/m, k = 100 N/m, fi = 1 Hz 12 = 2 Hz x(0) = 0.1 m (0) = 2 m/s Write a MATLAB scrip file that yields the following results: 1. [10] User is prompted to enter numeric values of m, c, k, fi, and f2. 2. (20) Given that the input force is a sine function, Find and display two analytical solutions for the two frequency values fand f2. The shown solutions should be easily readable (doesn't have stars), and numbers should be shown to 3 decimal places of precision. Hint: use vpa function. 3. [10] Plot the two solutions on one figure between t=0 and t= 5 s. Show proper axes labels with units, graph title, legend, and grid. 4. [20] On a separate figure and assuming f = fi, create three subplots of the following time functions: a. Spring force: Fs = kx b. Damper force: Fa = cử c. Mass energy: Em = m(x)2 d. Use proper titles for each subplot, axes labels with units, and grids. Hint: you can use either ezplot or fplot functions.