## Help for LRC Filter Applet

Reference to Java Components for Mathematics

Applet
This applet models a simple LRC circuit acting as a filter for a signal with two component frequencies. Most of the functionality is in place, but it has not been prettied up, given a full set of captions and had all color-coding made consistent.

Graphs
There are three graphs. The formula for each of them is given in the lines below the graphs. Each formula is given in the color of its respective graph.
1. Top left graph = input signal. It's labeled f(t) and its formula is given.
2. Bottom left graph = output or response . It's labeled V(t). It equals the voltage across the resistor and its formula is given.
3. Right graph = Amplitude response. It's labeled A(w) and its formula is given.
Note: in SecondOrder-LRC2.html the two left graphs are plotted on the same set of axes.

Controls and Values
1. All the sliders control the various parameters as labeled and shown in the formulas.
2. The dots on the input and response graphs correspond to time t. The values of f(t) and V(t) are printed between the two left hand graphs. The dots can be dragged with the mouse.
3. The dots on the amplitude response graph correspond to the settings for w1 and w2. The values of A(w1) and A(w2) are printed inside the amplitude graph window. The dots can be dragged with the mouse.
4. w0 is the practical resonance frequency. Its value is printed inside the amplitude graph window.

Known Bugs and Flaws
1. If R gets too small the amplitdue graph goes all wonky. This is caused by the small number of sample points used to plot the graph. As R goes to 0 the graph becomes too steep for this number of sample points.
2. The values printed in the graph windows are not color coded.
3. The formulas for A and Phi are given in a form that eliminates division by 0 in case one of the parameters or w are 0. It is not the most transparent form for seeing the resonant frequency.