(a) Use Laplace transforms to solve the differential equation given that = 0 and d/dt...

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(a) Use Laplace transforms to solve the differential equation

d0 +8 dr dt  + 160 = sin 2t

given that θ = 0 and dθ/dt = 0 when t = 0.

(b) Using Laplace transforms, solve the simultaneous differential equations

di, dt i + + 2i + 6i = 0 di, dt - 31 = 0

given that i1 = 1, i2 = 0 when t = 0.

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