Question: here is the question, be quick thanks Consider the differential equation (12 E? + W23; = cos(wt) wherew is a real number and w 75

here is the question, be quick thanks

Consider the differential equation (12 E? + W23; = cos(wt) wherew is a real number and w 75 :|:7r. Assume that y(0) = 0 and y'(0) = 0. (a) [5 points] The solution to this initial value problem is 1 y(t) = Wkoswt) cos(art)) Use the formula . a- . a+ cos or cos ,6 = 2 5111 2 5m 2 to write y(t) as a product of a real number and two sine functions. (b) [5 points] Suppose that the graph of y(t) is as follows. (The dashed lines are not part of the graph of 'y(t), but are there to help you solve this problem.) The y-axis is not drawn to the same scale as the t-axis. Assume that w > 11'. What is w? (c) [5 points] Now consider the differential equation cl2 y 2 + air = cos 1rt . Sketch the graph of any solution to this differential equation. (You do not need to nd the solution.) Your graph does not need to completely accurate. but you should label your t-axis with numbers

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