## 1.3 PRACTICE PROBLEMS

1. Find the combined values for resistors, capacitors and inductors in series and parallel.

2. Given the circuit below, find the transfer function. Simplify the results

2. a) Write the differential equations for the system pictured below.

b) Put the equations in input-output form.

3. Develop the differential equations for the system below, and use them to find the response to the following inputs. Assume that the circuit is off initially.

4. Find the input-output equation for the circuit below, and then find the natural frequency and damping coefficient.

5. Examine the following circuit and then derive the differential equation.

6. Consider the following circuit.

a) Develop a differential equation for the circuit.

b) Put the equation in state variable matrix form.

7. Examine the following circuit and then derive the differential equation.

8. Consider the following circuit.

a) Develop a differential equation for the circuit.

b) Put the equation in state variable matrix form.