a) Define unit step, unit ramp and unit impulse functions with necess…

Question

a) Define unit step, unit ramp and unit impulse functions with necessary mathematical and graphical representations. How these functions are related to each other? Explain. (11)

b) Find Laplace Transform of the following functions:

i) $f(t) = 5u(t-3) + 5t^2$

ii) $f(t) = 5[t\,u(t) + 6\delta(t-2)]$

iii) $f(t) = 6[t\,\delta(t-4) + 5\,u(t+2)]$ (3, 3, 3)

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