Laplace transform of sin(ωt – Φ)

[ch5497]

Hi,

I'm doing some preparation work for an upcoming mathematics module at University and I'm going over some Laplace transform questions.

Part of one question asks for the Laplace transform of sin(ωt – Φ) and after looking the transform up I've found the answer to be (ω)cos(Φ) + (s)sin(Φ) / (S^2 + ω^2).

Can anyone please tell me how to get there, because after attempting to transform using the normal method of integrating the function multiplied by e^-st I keep on hitting incorrect anwers.

Many thanks to anyone who can help me out with this - it's driving me crazy!


- Craig.

 

[Defennder]

You should derive the Laplace transforms of sin(wt) and cos(wt), then expand out sin(wt+a) in terms of sin/cos (wt) and then apply the Laplace transform linearly.