When we perform the preceding experiment the output we measure is a voltage (t) which is related to the cart position X(t) by the equation:

or

Thus our steady state output for an input is

We now wish to make a Bode plot of the magnitude (in decibels) of the output voltage corresponding to the cart position versus the frequency (in radians) of the input. The magnitude in decibels of (t) is

The Bode plot thus consists of three parts. First there is a constant gain term of This is a horizontal line on the Bode plot. Second, there is a pole at the origin with a gain of This is a line with slope of -20 DB/decade with a value of 0 DB at = 1 rad/sec. Third, there is a pole on the real axis at -B given by the term The magnitude of this at low frequencies is:

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and at high frequencies the magnitude is: | |||

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