Question

Find the Laplace transtorm of the
following function (1) f(t) = 6sin2t - 5 cosat (2)f(t)= t cos at
$f(t) = 6 \sin(2t) - 5cos2t$
$f(t) = t \cos(at)$
​

Answer 1

Answer:

1.$L(f(t))=\frac{12-5s}{s^2+4}$

2.$L(tcos at)=\frac{s^2-9}{(s^2+9)^2}$

Step-by-step explanation:

We are given that

a.$f(t)=6 sin 2t-5 cos 2t$

We have to find the laplace transform of given function

We know that L(sinat)=$\frac{a}{s^2+a^2}$

L(cosat)=$\frac{s}{s^2+a^2}$

$L(tcosat)=\frac{s^2-a^2}{(s^2+a^2)^2}$

Using the identities

1.F(s)=$6\cdot \frac{2}{s^2+4}-5\cdot \frac{s}{s^2+4}=\frac{12}{s^2+4}-\frac{5s}{s^2+4}$

F(s)=$\frac{12-5s}{s^2+4}$

2.f(t)=t cosat

Using the identity

$L(tcos at)=\frac{s^2-9}{(s^2+9)^2}$