Electric Circuit Analoges

Example 1.1

Draw the electrical circuit that is equivalent to the mechanical system shown. Determine the differential equation which describes the charge q in the circuit.

The differential equation that describes the motion of the system can be written in the following form. 

$$m\ddot{x}+c\dot{x}+kx={{F}_{0}}\cos \omega t$$

Using the Electric circuit analoges we can write the previous equation in the following form. 

$$L\ddot{q}+R\dot{q}+\left( \frac{1}{C} \right)q={{E}_{0}}\cos \omega t$$

Example 1.2

 Draw the electrical circuit that is equivalent to the mechanical system shown. What is differential equation which describes the charge q in the circuit?

The differential equation that describes the motion of the given mechanical system is:

$$m\ddot{x}+c\dot{x}+2kx={{F}_{0}}\cos \omega t$$

Using the Electric circuit analoges we can write the previous equation in the following form.

$$L\ddot{q}+R\dot{q}+\left( \frac{2}{C} \right)q={{E}_{0}}\cos \omega t$$

Example 1.3

Draw the electrical circuit that is equivalent to the mechanical system shown. Determine the differential equation which describes the charge q in the circuit

Differential equation which describes the motion of system can be written in the following form:

$$m\ddot{y}+c\dot{y}+ky=0$$

Using the table Electric circuit analoges we can derive the following equation.

$$L\ddot{q}+R\dot{q}+\frac{1}{C}q=0$$