Graphing a differential equation in mathematica?

[dangsy]

Homework Statement

I'm trying to graph a first order differential equation in Mathematica but the graph doesn't seem right when compared to my txt book. I'm using NDSolve.

The first order diff-eq is...

dy/dt' = -cy-sin(x)+fcos(z)

where z = omega t'

c = 0.05
f = 0.4
omega = 0.7

Time t' is the x-axis
and dx/dt' is the y-axis

The Attempt at a Solution

I have...

s = NDSolve[{\[Omega] x'[z] ==
y[z], \[Omega] y'[z] == -c y[z] - Sin[x[z]] + f Cos[z],
y[0] == -1, x[0] == 0}, {x, y}, {z, 0, 30}]

Plot[Evaluate[y[z] /. s], {z, 0, 30}, PlotRange -> All]

the graph should look akin to a cos function but the peaks are off compared to what's in my txt book.

Any ideas?

 

[Jhero]

Hi there, it looks like you are on the right track with your attempt at a solution. However, there are a few things that could be causing the discrepancy between your graph and the one in your textbook.

First, make sure that your initial conditions (y[0] == -1, x[0] == 0) are the same as the ones given in your textbook. Even a small difference in initial conditions can result in a significantly different graph.

Second, check your units. Are you using the same units for time and omega as in your textbook? If not, make sure to convert them to the same units before inputting them into your equation.

Third, try adjusting the range of your plot to match the range in your textbook. For example, if your textbook graph spans from 0 to 10, try plotting your graph from 0 to 10 as well.

If none of these suggestions solve the issue, it's possible that there may be a small error in your equation or in the way you are inputting it into Mathematica. Double check your equation and make sure all variables and operators are entered correctly.

I hope this helps! Let me know if you still have trouble and we can work through it together. Remember, troubleshooting is an important part of the scientific process, so don't get discouraged. Keep trying and you will eventually find the solution.