Question

Find a synchronous solution of the form A cos Qt+ B sin Qt to the given forced oscillator equation using the method of insertion, collecting terms, and matching coefficients to solve for A and B. y"+2y' +4y = 4 sin 3t, Ω-3 24 41 20 41 A solution is y(t)-os 3t-sin 3t

Answer 1

To find a synchronous solution of the form A cos Qt+ B sin Qt to the given forced oscillator equation, use the method of insertion, collecting terms, and matching coefficients to solve for A and B.

Step-by-step explanation:

To find a synchronous solution of the form A cos Qt+ B sin Qt to the given forced oscillator equation, we can use the method of insertion, collecting terms, and matching coefficients to solve for A and B. The forced equation is y"+2y' +4y = 4 sin 3t.

First, we differentiate the synchronous solution twice to get the second derivative. We then substitute this into the forced equation and collect like terms. By matching the coefficients of the sine and cosine terms, we can solve for A and B.

In this case, the solution is y(t) = A cos 3t - B sin 3t.