(a) Determine the inverse Laplace transform of

(b) The equation of motion of the moving coil of a galvanometer when a current i is passed through it is of the form

where θ is the angle of deflection from the ‘no-current’ position and n and K are positive constants. Given that i is a constant and θ = 0 = du/dt when t = 0, obtain an expression for the Laplace transform of θ.
In constructing the galvanometer, it is desirable to have it critically damped (that is, n = K).
Use the Laplace transform method to solve the differential equation in this case, and sketch the graph of u against t for positive values of t.

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