2D Graphs
Cassiopeia includes a sophisticated 2D graph module for plotting functions. We will discuss a damped LC tank in this document and then present the result of the derivation in a 2D graph. If you are not interested in the concrete physical problem skip the math and scroll down to the graphs. :-) We consider the following electrical circuit consisting of a capacitance, a resistor and an inductance.![]() |
This circuit is described mathematically by the following two differential equations:
![]() | (1) |
![]() | (2) |
The first equation can be rewritten as follows:
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We use the following approach to solve this linear differential equation:
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The last equation is true for all t only if we assume
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This gets us
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We consider the first solution and insert the expression into our solution apporach.
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We set
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and use Euler to rewrite
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The differential equation is linear. Therefore both summands must be a solution for the differential equations.
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A constant factor shouldn't harm a solution and the sum of two solutions is again a solution. We can thererefore write
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This can be transformed to
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We now use Eq. 2 to get an expression for the current in the circuit.
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We Alt-drag the expression for the angular frequency onto this last equation and replace Q with CU. This gets us the following two functions.
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Now choose SDM - FunctionGraph2D from the menu to insert a 2DGraph and drag the two equations onto the textview of the FunctionGraph2D inspector.
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The graph appears as follows In our document.
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We change the From: and To: values for the abscissa to 0 - 100 ms. After modifying the values press <Return> in one of the fields to trigger redraw of the graph.
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Now change the coefficients C, L and R to more realistic values. Also check the Fine box to get a more accurate rendering of the graph.
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Choose Tools - Colors from the menu and drag red color onto the current function in the tablevie win the lower left and blue color onto the function for the voltage.
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This does not look too bad. However, the current line is too flat to be easily examined. We therefore specify a scale factor of ten for the current function.
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Click back into your document. The graph is updated accordingly.
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We are not done yet. Let's assume we are interested in the heat loss in the wire resistance. This loss is given by
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We Alt-drag the expression for the current onto this equation and get
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We now double-click onto the 2D graph to (re)open its inspector and simply drag this last equation onto the textview. We also drag the expression for

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Clicking back into the document updates the 2D graph.
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The functions in a 2D graph can be interdependent. Assume the result of your creative work is the following set of functions (see Example Paper):
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Note that the last function depends on all the other. These functions can be dragged as they are onto a 2D graph to be plotted.
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