Question

4. Two functions are given below. For the questions below, answer a, b, neither, or both, whichever is appropriate a. F(s)+40+400 b. F(s)=ー10,+400 1) Which function/s would include an impulse function in the time domain? 2) Which function/s would contain a damped sinusoid in the time domain? 3) Which function/s would have a final value of zero? s+10s+400

Answer 1

F(s) = 100 [s^2 + 105 + 400 -105 -400]/s^2 + 105 + 400 = 100 [s^2 + 105 + 400]/s^2 + 105 + 400 -100 [105 = 400]/s^2 + 100 + 400 = 100 - 100 [105 + 400/s^2 + 105 + 400 lim_s rightarrow infinity s times 100 s^2/s^2 + 105 + 400 = infinity only par (a) has final value zero s(t) in time domain only function (b) include impale is time domain. S^2 + 105 + 400 = 0 2 w-n = 10, w^2_n = 400, w-n = 20 = 10/2 times 20 = 1/4 < 1 s^2 + 400 + 400 = r 2 w_n = 40, w_n = 20 = 1 dropped sinusoid lim_s rightarrow infinity s 1400/s^2 + 40 s + 400 = lim_s rightarrow infinity 100/s(1 + 40/s + 400/2) = 0