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The position x(t), of a damped oscillator with forcing satisfies the ordinary differential equation , i)...

The position x(t), of a damped oscillator with forcing satisfies the ordinary differential equation ,

i) where f(t) denotes the forcing on the oscillator. (i) If x(0) = 0, dx dt (0) = 1, f(t) = 4t and the Laplace transform of x(t) is denoted X(s) = L[x(t)], then show that

X(s) = 1 /(s + 2)^2 + 4 /s^2 (s + 2)^2

ii) Hence find x(t)

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