## Module 6 Homework Assignment

- Determine the magnitude and phase of the output from the following system when subject to a sinusoidal input of 2sin(4𝑡). Write the steady-state sinusoidal output.

𝐺(𝑠)=3 (𝑠+2) - Determine the gain in dB for the following

a. 0.5

b. 15

c. 0.1

d. 30 - Use MATLAB to create the Bode plot of the following system. First break down the system into five (5) simpler elements. Include this broken down transfer function in your homework. Plot all five elements plus the full system on the same Bode plot. Include the MATLAB commands used and the resulting plot.

𝐺(𝑠)=24𝑠^2/ 𝑠(𝑠+2)(𝑠+4) - Use MATLAB to find the stability measures for the following system. Provide the Bode plot and answer “How can you tell that the system is stable from the Bode plot?” Include grid lines in your Bode plot. Provide the Bode plot with the stability measures plotted on it. Include the MATLAB commands used.

80/ 𝑠(𝑠+4)(𝑠+10) - Use MATLAB to create the Nyquist diagrams for the following open-loop transfer function when K=100 and K=400. Plot both systems on the same Nyquist diagram and answer “How can you tell that the system is stable or unstable from the Nyquist diagram?” Include the MATLAB commands used.

𝐾/((𝑠+2)(𝑠+7)(𝑠+1))