f(t)=3sin(t)+5cos(3t)
i am not familiar with laplace of sin and cos functions
anyone help?
Table of Laplace Transforms
Particularly,
$\displaystyle \mathcal{L}(\cos(ax)) = \frac{s}{s^2 + a^2}$
$\displaystyle \mathcal{L}(\sin(ax)) = \frac{a}{s^2 + a^2}$
$\displaystyle \mathcal{L}(c*f(t)) = c*\mathcal{L}(f(t)) \, \text{for any} \, c \in \mathbb{R} $
Ive just tried to answer the question ...I would like to know if the answer i found is right..
Qn: laplace of (f(t)=3sin(t)+5cos(3t))
L{f(t)}=3L{sin(t)}+5L{cos(3t)}
=3(1/(s^2+1))+5(s/(s^2+9))
On further simplification
=5s^3+3s^2+5s+27/(s^2+1)(s^2+9)