The Bode Plot

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

          p15_1a           or           p15_1b

Thus our steady state output for an input acoswt is p15_2

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 vsubx(t) is

           p15_3a p15_3b

The Bode plot thus consists of three parts. First there is a constant gain term of p15_7a This is a horizontal line on the Bode plot. Second, there is a pole at the origin with a gain of p15_7b This is a line with slope of -20 DB/decade with a value of 0 DB at omega = 1 rad/sec. Third, there is a pole on the real axis at -B given by the term p15_7c The magnitude of this at low frequencies is:

           p15_8            (omegagtb)
and at high frequencies the magnitude is:
p15_9 (omegagtb)