What is laplacetransform f(t)=7sin((3t)/2) ?

The answer to laplacetransform f(t)=7sin((3t)/2) is (42)/(4s^2+9)

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laplacetransform f(t)=7sin((3t)/2)

laplace transform

f (t) = 7 sin (\frac{3 t}{2})

\frac{42}{4 s ^{2} + 9}

Solution steps

L {7 sin (\frac{3 t}{2})}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 7 L {sin (\frac{3 t}{2})}

L {sin (\frac{3 t}{2})} : \frac{6}{4 s ^{2} + 9}

= 7 \cdot \frac{6}{4 s ^{2} + 9}

Refine

7 \frac{6}{4 s ^{2} + 9} : \frac{42}{4 s ^{2} + 9}

= \frac{42}{4 s ^{2} + 9}

x \to - 1 lim (- x^{2} - 2 x + 3)

(4 x y^{2} - 3) d x + (4 x^{2} y + 4) d y = 0

\frac{d}{d x} (sin (x^{3} + y^{2}))

\frac{\partial}{\partial x} (\frac{1}{( x + y )})

\int 4 t^{4} e^{6 t^{5}} d t

What is laplacetransform f(t)=7sin((3t)/2) ?
The answer to laplacetransform f(t)=7sin((3t)/2) is (42)/(4s^2+9)