How do you think this will change for omega = 1.05? (Keeping the damping zero.)
Try it! (You can adjust the driving force to scale the curve.) Then try 1.025. How, exactly, has the pattern changed?
What happens at omega = 0.9? Check it out. How does this curve differ from the omega = 1.1 curve? Or does it?
Now do omega = 1, but now add damping b = 0.08.
Explore different values of damping, but adjust the driving force strength so the pattern is a reasonable size on the screen.
Show you can choose the initial position and velocity so that the oscillations initially decrease in magnitude.
Can that be done for driving at the resonant frequency? Check it out!
What curve do you expect if you put the spring constant k = 0?
What about k = 0 and F = 0? (Put b nonzero.) Try nonzero initial position, zero and nonzero initial velocities.
Is that what you expect from looking at the equation?
Here's the relevant lecture.
Program by: Carter Hedinger