Find laplace transform of each following a) displaystyle{t}^{n} b) displaystyle cos{omega}{t} c) displaystyle sin{{h}}{left({c}{t}right)} d) displaystyle cos{{h}}{left({c}{t}right)}

Question

Find laplace transform of each following
a)

t^{n}

b)

\cos ω t

c)

\sin h (c t)

d)

\cos h (c t)

Answer 1

ANSWER FOR (A)We have to find Laplace transform of

t^{n}

, that is,

L {t^{n}}

.
Now from the Laplace Transform table we know that

L {t^{n}} = \frac{n!}{s^{n + 1}}

This shows that

L {t^{n}} = \frac{n!}{s^{n + 1}}

ANSWER FOR (B) We have to find Laplace transform of

\cos (ω t)

, that is, L

{\cos (ω t)}

Now from the Laplace Transform table we know that

L {\cos (a t)} = \frac{s}{s^{2} + a^{2}}

Whis shows that

L {\cos (ω t)} = \frac{s}{s^{2} + ω^{2}}

ANSWER FOR (C) We have to find Laplace transform of

\sin h (c t)

, that is, L

{\sin h (c t)}

Now from the Laplace Transform table we know that

L {\sin h (a t)} = \frac{a}{s^{2} - a^{2}}

Whis shows that

L {\sinh (c t)} = \frac{c}{s^{2} - c^{2}}

ANSWER FOR (D) We have to find Laplace transform of

\cos h (c t)

, that is, L

{\cos h (c t)}

Now from the Laplace Transform table we know that

L {\cos h (a t)} = \frac{s}{s^{2} - a^{2}}

Whis shows that

L {\cos h (c t)} = \frac{s}{s^{2} - c^{2}}

Want to know more about Laplace transform?