ke X m Cdx met or Part 1. An engine suspension structure is idealized as a damped spring-mass system with stiffness k = 10 kN/m; mass m = 100 kg; and damping coefficient c = 200 Ns/m. During the engine operation, the system is subjected to a harmonic force of amplitude Fo = 10 kN at frequency f = = 4 Hz. 20 The response of this system under forced excitation is described by the following equation: F(t) = F, sin(wt) d2 me = F(t) kx-case de EF, sin(wt) doa 1. Solve the equation numerically and plot the response x(t) of the system for the first 6 sec of the harmonic force application (or for the first 20 cycles of the harmonic force action). Assume the following initial conditions: x(0) = 0, d. (C) = 0 (the system is in an k equilibrium before the force application). 2. Calculate (t) response by numerical differentiation of the obtained x(t) solution and plot both (t) and X(t) in the same graph window. m X dx C = . Create a MATLAB code which is capable of performing the following: Solving the equation 1 by using either (a) an original code employing one of the standard methods for solving differential equations, or (b) a built-in MATLAB solver. [(a) 50 marks or (b) 20 marks] Plotting the solution x(t) for the first 6 sec in the graph window. Providing the graph with title, axis labels, scales and units, and data legend. [5 marks] Calculating (t) by numerical differentiation of the obtained X(t) solution by using either (a) an original code employing one of the standard methods for numerical differentiation, or (b) a built-in MATLAB command. [(a) 30 marks or (b) 10 marks] Plotting both at (t) and X(t) in the same graph. Providing the graph with title, axis labels, scales and units, and data legend. [5 marks] dar dt The MATLAB code should be fully commented. [10 marks]