Consider the differential equation m??x + c?x + kx = f (t ) , where m = 10 kg, c
ID: 2942602 • Letter: C
Question
Consider the differential equation m??x + c?x + kx = f (t ) , where m = 10 kg,c = 1 kg/s, k = 7 N/m, f (t ) = F sin(?t ) , F = 3 N, and ? = 1 / 3 rad/sec. Initial
conditions are x(0) = 1 m and ?x(0) = -1 m/s.
(A) Obtain the exact analytical solution to this differential equation and initial
conditions.
(B) Use Matlab to numerically evaluate and plot the exact solution obtained in (A)
above. Be very careful to select an appropriate range for time t in order to capture the
response of interest.
(C) Use ode45 to numerically integrate the differential equation for the initial
conditions. For the two solution methods in (B) and (C) above, compare and plot on the
same graph the two solutions for x(t ) . Make a similar separate comparison plot for ?x(t ) .
(D) Generate the phase plot of x(t ) versus ?x(t ) .
Explanation / Answer
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