Question

Calculate the Laplace transforms of the following from the definition. 1. y = t^2. y = t^3

Answer 1

Answer:

1) $L(y)=\frac{2}{s^{3}}$

2) $L(y)=\frac{6}{s^{4}}$

Step-by-step explanation:

To find : Calculate the Laplace transforms of the following from the definition ?

Solution :

We know that,

Laplace transforms of $t^n$ is given by,

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

1) $y=t^2$

Laplace of y,

$L(y)=L(t^2)$ here n=2

$L(y)=\frac{2!}{s^{2+1}}$

$L(y)=\frac{2}{s^{3}}$

2) $y=t^3$

Laplace of y,

$L(y)=L(t^3)$ here n=3

$L(y)=\frac{3!}{s^{3+1}}$

$L(y)=\frac{3\times 2}{s^{4}}$

$L(y)=\frac{6}{s^{4}}$