Question

Find f(t) for the function F(s): 135/(s+3)³

Express your answer in terms of u(t), (t), and t. Enter the phase angle in radians. Express your answer using three significant figures.
F(t)=_____________

Answer 1

The given function F(s) is solved for f(t) by applying the inverse Laplace transform. The result is f(t) = 67.5t^2e^(-3t)u(t), which is a non-oscillatory function without a phase angle in radians.

Step-by-step explanation:

To find the function f(t) for the given F(s) which is 135/(s+3)³, we need to apply the inverse Laplace transform. The inverse Laplace transform of 1/s^n is t^(n-1)/(n-1)! multiplied by the unit step function u(t). In our case, n equals 3.

Therefore, the inverse Laplace transform of 135/(s+3)³ is:

f(t) = 135 * t^(3-1)/(3-1)! * e^(-3t) * u(t)

f(t) = 135/2 * t^2 * e^(-3t) * u(t)

Expressed using radians, there is no phase angle in this function because it is not an oscillatory function.

Hence, f(t) = 67.5t^2e^(-3t)u(t)