1. The systems below have a variable spring coefficient. For each of the systems below,
a) Write the differential equation and convert it to a transfer function.
b) If the input force is a step function of magnitude 1N, calculate the time response for ‘y’ by solving a differential equation for a Ks value of 10N/m.
c) Draw the poles for the transfer function on a real-complex plane.
d) Draw a Bode plot for Ks = 1N/m.
2. Draw a root locus diagram for the feedback system below given the variable parameter ‘P’.
3. For the transfer functions below, draw the root locus plots assuming there is unity feedback, i.e., H(D) = 1. Draw an approximate time response for each for a step input.
4. Draw a root-locus plot for the following feedback control systems.