The Equation of motion for the standard mass-spring-dampersystem is
MẠ+ Bẋ + Kx = f(t).
Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m},determine the free response of the system to initial conditions {x0 = -1m, v0 = 40 m/s}. To help verify thecorrectness of your answer, a plot of x(t) should go through thecoordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03,-0.2043}.
determine the steady-state response of the system to sinusoidalinputs of unit amplitude at specified frequencies. You may use anyinitial conditions you wasn’t for this section. Use the followingfrequencies: ω = {0.2, 1, 6, sqrt (200), 20, 100, 1000} rad/s.
Modify your Matlab code to numerically simulate the response ofthe system to the frequencies listed above. Simulate one frequencyat a time. Simulate for a sufficient time that the system will haveattained steady state. Plot three periods of the systems’s responseat steady state (so the initial time value on the plot will not bet = 0). Then estimate the amplitude of the response for eachfrequency; you should have seven amplitudes when you are done.
Make a second plot where you plot the amplitudes determinedabove against the frequencies (make a frequency response magnitudeplot). The x-axis should be logarithmic and the y-axis should be indB. CLEARLY LABEL YOUR AXES. For the plot, connect the points withsolid black lines with a LineWidth of 3.
Evaluate │H(jω)│ for the frequencies: ω = {0.25, 1.5, 6.5, 15,25, 150, 800} rad/s. Do this BY HAND. Clearly show your work. Thenplot the resulting {ω, │H(jω)│} points as green diamonds usingMarkersize of 10 and LineWidth of 3.
