3. (21) Take the time derivative of $(t) = Acos(wt + (1)) (that is, calculate (ix/cit) to nd an equation for v(t). Hint: you will need to know the derivative of the cosine function (is well as the \"chain rule". (b) Draw the function v{t) with (25 = O. (c) Calculate the total mechanical energy of the system (E = K + U) using your expressions for $05) and v(t). Simplify your expression as much as possible. (Hint: You wit! need to use the following identity: cos2(wt + gt) + sin2 (wt + qt) 2 1.)