plotting linear differential equations and using a bode plot for amplitude and frequency

I have two linear differential equations

a) 1.896(dy(t)/dt) = x(t)

b)

I am having issues correctly inputting this into matlab to be able to plot this on a bode amplitude and frequency diagram.

[William Rose]

@Tiffany So,

Are a) and b) a coupled set of equations, or two separate problems?

There are many approaches to generating a Bode plot. Two popular ones are:

1. Find an analtyic solution to the differential equation, and use that analytic solution to determing the equations for the magnitude and phase of the Bode plot.

2. Solve the differential equation numerically, with a sinusoidal input of some specific frequency. Determine the magnitude and phase relation between input and output, once the system stabilizes. That generates one magntiude point and one phase point for your Bode plot. Repeat with other frequency inputs, until you have done enough points to make a plot that you are satisfied with.

Do you want to do method 1, or method 2, or something else?

[Tiffany So]

Hi William! these are two separate equations and i need to graph both separately. i will try both methods, thank you for the suggestion!

Answer 1

[Sulaymon Eshkabilov]

It is a quite straightforward exercise and no need to solve for an analytical solution. Convert to "s" domain (Laplace transform) and create tf, then use bode(). Your exercise problems are not sufficiently defined.

E.g. (b) Assuming "0" initial conditions,

TF_b = tf(130.19, [1 8.22 130.19]);
bode(TF_b)

[Tiffany So]

that is perfect, thank you very much Sulaymon!

[Sulaymon Eshkabilov]

Most welcome!