Question

Use the Laplace transform to solve the following equation 1. Find the solution to the following second-order-system. Provide the solution in the time domain y(t). Use the Laplace tables uploaded on Canvas to help you with the inverse transform back into the time domain. y¨​+3y˙​+yy(0)y˙​(0)​=1=0=1​

Answer 1

To solve the second-order system using the Laplace transform, we take the Laplace transform of the equation, solve for Y(s), and then find the inverse transform to obtain the solution in the time domain.

Step-by-step explanation:

To solve the given second-order system using the Laplace transform, we first need to take the Laplace transform of the equation. Let Y(s) represent the Laplace transform of y(t). Applying the Laplace transform to each term of the equation, we get s^2Y(s) + 3sY(s) + y(0)s + y'(0) = 1/s^2.

Next, we rearrange the equation to solve for Y(s): Y(s) = (1 - y(0)s - y'(0))/(s^2 + 3s).

Now, using the Laplace transform table, we find the inverse transform of Y(s) to obtain the solution in the time domain, y(t).