# Engineering Acoustics/Solution Methods: Electro-Mechanical Analogies

After drawing the electro-mechanical analogy of a mechanical system, it
is always safe to check the circuit. There are two methods to accomplish
this:

## Review of Circuit Solving Methods

**Kirchkoff\'s Voltage law**

\"The sum of the potential drops around a loop must equal zero.\"

![](KVL.png‎ "KVL.png‎")

$v_1 + v_2 + v_3 + v_4 = 0 \displaystyle$

**Kirchkoff\'s Current Law**

\"The Sum of the currents at a node (junction of more than two elements)
must be zero\"

![](KCL.png‎ "KCL.png‎")

$-i_1+i_2+i_3-i_4 = 0  \displaystyle$

**Hints for solving circuits:**

Remember that certain elements can be combined to simplify the circuit
(the combination of like elements in series and parallel)

If solving a ciruit that involves steady-state sources, use impedances.
Any circuit can eventually be combined into a single impedance using the
following identities:

Impedances in series: $Z_\mathrm{eq} = Z_1 + Z_2 + \,\cdots\, + Z_n.$

Impedances in parallel:
$\frac{1}{Z_\mathrm{eq}} = \frac{1}{Z_1}  +   \frac{1}{Z_2}  + \,\cdots\, +  \frac{1}{Z_n} .$

## Dot Method: (Valid only for planar network)

This method helps obtain the dual analog (one analog is the dual of the
other). The steps for the dot product are as follows: 1) Place one dot
within each loop and one outside all the loops. 2) Connect the dots.
Make sure that only there is only one line through each element and that
no lines cross more than one element. 3) Draw in each line that crosses
an element its dual element, including the source. 4) The circuit
obtained should have an equivalent behavior as the dual analog of the
original electro-mechanical circuit.

**Example:**

![](Dotmethod.jpg "Dotmethod.jpg")

The parallel RLC Circuit above is equivalent to a series RLC driven by
an ideal current source

## Low-Frequency Limits

This method looks at the behavior of the system for very large or very
small values of the parameters and compares them with the expected
behavior of the mechanical system. For instance, you can compare the
mobility circuit behavior of a near-infinite inductance with the
mechanical system behavior of a near-infinite stiffness spring.

                  Very High Value   Very Low Value
  --------------- ----------------- ----------------
  **Capacitor**   Short Circuit     Open Circuit
  **Inductor**    Open Circuit      Closed Circuit
  **Resistor**    Open Circuit      Short Circuit

Back to Main page
