Consider the following differential equation i(t) + 9: (t) + 14x(t) = 0.12(t), where r(t) is the output displacement, the input force f(t) is a unit step function, and the initial conditions are given by *(0) = (0) = -0.04 m 0.01 m/s answer the following questions: (a) (2 points) convert the ode to laplace domain, considering the non-zero initial conditions. find the laplace transform x(s) of the displacement (t). notice that f(s) is known since f(t) is given. (b) (3 points) using matlab residue command, obtain the residues and the poles, and obtain (t) by taking the inverse laplace of x($). (c) (1 points) is the solution (t) found in step (b) energy dissipating? if it is, (t) must eventually go to a step wlue consistent with the input. does it? why, why not? (d) (4 points) plot in matlab the analytical form of (t) found in the previous step as a function of time (see the gray box below). next, construct the functional block diagram of this dynamics using integrators (1/8) in simulink. in each integrator, insert the corresponding initial condition to simulate (t). compare this simulation with the analytical result obtained. when an integrator output is displacement (or, velocity), then displacement (or, velocity) initial condition can be inserted into that integrator. double click the integrator to enter the initial condition in the text bor. to plot the function () = 4 sin(101) in matlab, define the time vector first: time = [0: 0.01: 10]: which creates a set of time stamps, from 0 to 10 sec, with a step size of 0.01. next define the function, f = 4*sin(10%t); and finally execute the plot command: plot(t. f,'*') which will plot each data point with a symbol and interpolate between them with lines.