Figure shows a thermal second-order system with input u(t) and output y(t). The temperature output is converted by a transducer, modeled as a first-order lag, to an electronic signal v(t).  a.Find the...

Figure shows a thermal second-order system with input u(t) and output y(t). The temperature output is converted by a transducer, modeled as a first-order lag, to an electronic signal v(t).

a.Find the exact solution for the unit step response of v(t).

b. Find the stiffness ratio relating the ratio of the largest to the smallest (in magnitude) characteristic root of the system. Is the system stiff?

c. Simulate the unit step response with a fixed-step RK integrator. What is the largest integration step size that can be used to obtain a stable solution?

d. Repeat part (c) using one of Simulink’s stiff integrators, and compare the number of steps used by the RK and stiff integrator.

e. Compare the frequency response function V(jω))/U(jω) with and without the sensor dynamics by generating a Bode plot for each on the same graph. Comment on the results.