Question

Dynamics

Problem 3. ODES to op-amp circuits - NOTE: THIS ONE WON'T BE GRADED OR ON THE TEST, but I think it is a really great exercise of how to implement an ODE as a circuit. Implement the following ODE using op-amp circuits. The easiest way to do this is to find the block diagram of the ODE using the technique show in Section 4.5.3 of the textbook. This should leave the ODE described as a block diagram with (1) integrators, (2)constant scale factors, (3) feedback with summation. You should be able to implement each one of these with an op-amp circuit. Hint: Certain op-amp circuits can only be implement having a negative gain (e.g. inverting configuration). So, you will need to be extra careful about keeping track of the signs of various signals within your system.

\frac{d^{2} V_{o}(t)}{d t^{2}}-15 \frac{d V_{o}(t)}{d t}+100 V_{o}(t)=V_{i}(t)+2 \frac{d V_{i}(t)}{d t}