In the given shear stress versus strain rate graph:
- Pseudo-plastic fluids (X) show a decrease in viscosity with increasing shear rate.
- Newtonian fluids (Y) exhibit a constant viscosity, meaning the shear stress is directly proportional to the strain rate.
- Dilatant and thixotropic fluids exhibit changes in viscosity with different shear rates, but not in the way described by this graph.
Conclusion: Option (a) correctly identifies the fluid properties for X and Y.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.