Question

Define Heaviside unit step function. Using unit step function find the laplace transform of:

f (t) = {(sint, 0 ≤ t < π) (sin2t, π ≤ t < 2π) (sin3t, t > 2π)

Answer 1

The given f (t) can be written in the following form by a standard property. 

f (t) = sint + [sin2t – sint] u(t – π) + [sin3t – sin2t] u(t – 2π) 

Now L [f (t)] = L (sint) + L {[sin2t – sint] u(t – π)} + L{[sin3t – sin2t] u(t – 2π)} ...(1) 

Consider L [sin2t – sint] u(t – π)