x(0) = 0 a. 0.3 cos(t) + 0.1 sin(t) – 0.3 e-3t b. 0.3 cos(t) + 0.1 sin(t) – 0.3

Question

                              x(0) = 0
a. 0.3 cos(t) + 0.1 sin(t) – 0.3 e-3t
b. 0.3 cos(t) + 0.1 sin(t) – 0.3
c. 0.3 cos(t) – 0.3 e-3t
d. 0.2 cos(t) + 0.2 sin(t) –0.2 e-3t

Explanation / Answer

given , dx/dt + 3*x = cost. -------->equation 1. x(0) = 0 dx/dt at x=0 is : cos(0) - 3*0 = 1 for (a) : x(0) =.3cos(0) + 0.1sin(0) - .3e^(0) = 0 x'(0) = -.3sin(0) +0.1cos(0) +0.9e^(0) = 1. for (b) : x(0) =.3cos(0) + 0.1sin(0) - .3 = 0 x'(0) = -.3sin(0) +0.1cos(0) + = .1 for (c): x(0) =.3cos(0) + 0.3sin(0) = 0.3 for (d) : x(0) =.2cos(0) + 0.2sin(0) - .2e^(0) = 0 x'(0) = -.2sin(0) +0.2cos(0) +0.6e^(0) = 0.8 hence option (a) is the correct answer

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