What is laplacetransform 3sin(4t) ?

The answer to laplacetransform 3sin(4t) is (12)/(s^2+16)

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laplacetransform 3sin(4t)

laplace transform

3 sin (4 t)

\frac{12}{s ^{2} + 16}

Solution steps

L {3 sin (4 t)}

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)}

= 3 L {sin (4 t)}

L {sin (4 t)} : \frac{4}{s ^{2} + 16}

= 3 \cdot \frac{4}{s ^{2} + 16}

Refine

3 \frac{4}{s ^{2} + 16} : \frac{12}{s ^{2} + 16}

= \frac{12}{s ^{2} + 16}

\frac{d}{d x} (cos (x^{l n (x^{2} + 1)}))

x \to 0 lim (\frac{x - x}{x})

8 x^{^{''}} + 8 x^{^{'}} + \frac{1}{4} x = 0, x^{^{'}} (0) = 1, x (0) = 2

\frac{d}{d x} (\frac{2 x}{1 - x})

x \to 0 lim (\frac{0}{x})

What is laplacetransform 3sin(4t) ?
The answer to laplacetransform 3sin(4t) is (12)/(s^2+16)