Question

find L[sin 3t sin 2t]​

Answer 1

Step-by-step explanation:

As the Laplace transform is a linear operator, we can take the transform of each part of this expression and subtract them.

Transform of 0.5cos(t)=s/(2s2+2)

Transform of 0.5cos(5t)=s/(2s2+50)

s/(2s2+2)−s/(2s2+50)=12s/(s4+26s2+25)

Answer 2

We need to recall the following folmuals to solve problem

1. Sin(A)sin(B) = {cos(A-B)- cos(A+B)}/2

2. $L({cos(at)}) = \frac{s}{s^2+a^2 }$

This pro is about the Laplace equation

Given expression  [sin 3t sin 2t]

We have to find the Laplace transformation of the given expression.

First simplify the expression .

$sin 3t sin 2t= \frac{cos (3t-2t)-cos (3t+2t)}{2}$

                 = cos(t)/2 - cos(5t)/2

Now find Laplace transformation

L{cos(t)/2 - cos(5t)/2} = L{cos(t)/2} - L{cos(5t)/2}

                                  $=-\frac{1}{2} \cdot \frac{s}{s^{2}+25}+\frac{1}{2} \cdot \frac{s}{s^{2}+1}$

Simplify

$-\frac{1}{2} \frac{s}{s^{2}+25}+\frac{1}{2} \frac{s}{s^{2}+1}=\frac{12 s}{\left(s^{2}+1\right)\left(s^{2}+25\right)}$