Question

Find the Laplace transform of f(t)=integral of (t-torque)^2 cos 2*torque d*torque from 0 to t.

Answer 1

Does "torque" stand for tau, \(\tau\) ?

Answer 2

Yes.

Answer 3

\[f(t)=\int_0^t (t-\tau)^2\cos2\tau~d\tau\]
Apply the convolution theorem:
\[\mathcal{L}\left\{\int_0^t f(t-\tau)g(\tau)~d\tau\right\}=F(s)G(s)\]
Here, \(f(t)=t^2\) and \(g(t)=\cos(2t)\). So, the Laplace transform of the integral is
\[\mathcal{L}\left\{t^2\right\}\mathcal{L}\left\{\cos(2t)\right\}\]

Answer 4

Hmm, maybe that's not the convolution theorem... well, whatever it's called, use that formula.

Answer 5

Sorry, but I don't understand what you wrote above. The processing math is 0%.