Question

find the laplace transform of the following function f(t)=6sin2t-5cos2t​

Answer 1

d'f(t) = 6cos 2t(2)+5sin 2t(2)

= 12cos 2t + 10sin 2t

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Answer 2

The laplace transformation of f(t) is  $L(f(t))= \dfrac{12-5s}{s^2+4}$

Step-by-step explanation:

To find : The Laplace transformation of  f(t)= 6sin2t-5cos2t

Now let L denotes the Laplace transformation

f(t)= 6sin2t-5cos2t

taking Laplace

L(f(t)) = L(6sin2t-5cos2t)

Now By Laplace linearity we have

L(f(x)+a(g(x)))= L(f(x)+aL(g(x))

so

L(f(t))=L(6sin2t-5cos2t)

now as we know

$L(\sin at)= \dfrac{a}{s^2+a^2} \text { and } L(\cos at)= \dfrac{s}{s^2+a^2}$

Therefore we get

$L(f(t))= 6 L(\sin 2t)-5L(\cos 2t)\\\\\Rightarrow L(f(t))= 6(\dfrac{2}{s^2+2^2} )-5(\dfrac{s}{s^2+2^2} )\\\\\Rightarrow L(f(t))= (\dfrac{12}{s^2+4} )-(\dfrac{5s}{s^2+4} )\\\\\Rightarrow L(f(t))= \dfrac{12-5s}{s^2+4}$

Hence the Laplace transformation is  $L(f(t))= \dfrac{12-5s}{s^2+4}$

#Learn more

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)  

brainly.in/question/12285998

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