Step 1: Understanding the Arrhenius Equation
The Arrhenius equation expresses the relationship between the rate constant and temperature, as follows: \[ k = A \cdot e^{-\frac{E_a}{RT}} \] where: - \( k \) = rate constant - \( A \) = frequency factor - \( E_a \) = activation energy - \( R \) = universal gas constant - \( T \) = temperature
Step 2: Conclusion
The Arrhenius equation primarily shows the variation of the rate constant with temperature.
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.