How do you think this will change for m = 0.5 and k = 0.5?
Try it! Then try both equal to 1. How, exactly, has the critical damping changed?
What happens at m = 1 and k = 0.25? Check it out. How does this critical damping differ from m = 0.5 and k = 0.5? Or does it?
Here's the relevant lecture.
Program by: Carter Hedinger