I need help in Q 26,29,30,31 The pole-zero plot of a transfer function is given

Question

I need help in Q 26,29,30,31

The pole-zero plot of a transfer function is given in figure 26(a) below. Here sigma 1 = 2, sigma 2 = -2, sigma 3 = -4 , and omega 1 = 4. If lim s rightarrow H(s) = 20 ,find H(s). Construct a general input which will cause the response to be unbounded (unstable). Compute the impulse response. Figure 26 Repeat part (a) for the pole-zero plot of figure 26(b). Same values for sigma and omega 1 with the zero at the origin a double zero. If H(4) = 2, find H (s). Construct a general input which will cause the response to be unbounded (unstable). Compute the impulse response. Chapter 14, Problem 17, Page 745 Chapter 14, Problem 23, Page 747 Using your newly developed knowledge of sinusoidal steady state via transfer functions, answer each of the following questions: A circuit has transfer function The circuit is excited by a sinusoidal input vin(t) = 2 cos (5 t)u (t) V. Compute the magnitude and phase of the STEADY STATE output voltage. Write down the steady state output voltage sinusoid. A circuit with transfer function is excited by the input vin(t) = cos (100t + 10 degree) V. Compute the magnitude and phase of the STEADY STATE output voltage. Write down the steady state output voltage sinusoid. A circuit with transfer function is excited by the input Vin(t) = 5cos (5t + 45 degree ) V. Compute the magnitude and phase of the STEADY STATE output voltage. Write down the steady state output voltage sinusoid.

Explanation / Answer

Looking at the graph and the 1st point given,

the general equation is :

H(s) = 80(s)(s-2)/(s+2)(s+4)

Inputs s=-2,-4 will make the system unstable as the output will be infinite, which is unstable

For the next part with H(4) = 2,

H(s) = 3(s)(s)(s-2)/(s+2)(s+4)

For unstability, the answer remains same as the poles are same.

Hope it was helpful :)

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