Question

find the laplace transform of f(t)= sin 8t sin 6t

Answer 1

integrate the equation in the form of integral from + infinity to negative infinity ,,,,,,,,,,,to the Ft) .e^-xt

Answer 2

Consider the trig identities cos(A-B)≡cosAcosB+sinAsinB and cos(A+B)=cosAcosB-sinAsinB.

Therefore cos(A-B)-cos(A+B)≡2sinAsinB, and sinAsinB≡½(cos(A-B)-cos(A+B)).

Let A=8t and B=6t, then f(t)=½(cos(2t)-cos(14t)).

The Laplace Transform of cos(at)=s/(s²+a²).

So F(s)=½[s/(s²+4)-s/(s²+196)].

This can also be written F(s)=s(s²+100)/((s²+4)(s²+196)).