Mass-Spring Systems 2: Underdamped Motion

ODEs: Consider the mass spring system governed by the IVP x"+2x'+5x = 0, x(0)=1, x'(0)=0. Using the solution to the IVP, we describe the motion of the system and plot the trajectory in the phase plane. Then we use certain solutions to describe the entire phase portrait. We also note the connection to the slope field.

[ffrgtm]

I really like this method a lot more than the b=2lambda crap in my book... also my book uses (for critical damped) lambda squared = omega squared (where omega squared = C in your video). Basically I had no idea what was going on until watching this. Thanks man!

[MathDoctorBob]

@ffrgtm You're welcome, and thanks for the comment! These spring examples are a ton of fun to teach, but it's easy to get lost in the details. I always pick up something new. - Bob

[joeschmo]

What is that black stick he's holding, a piece of beef jerky?

[chiledu]

thank you! i watched your other videos in differential equation as well, and you helped me understand some of the confusion. if i pass my class this semester i ill buy u food or beer haha.

[zuhzuhbeer]

setting the equations by sin(2t) and cos(2t)
then squaring both and by adding their squares it would be equal to 1

[ZachSchultzM]

Hey, I'm confused on how you found (x + (1/5)x')^2 + ((2/5)x')^2 = e^-2t, can you give me a bit more explanation please?

Thanks for the video too!

[concisestem]

Any chance you'll do a video on forced vibrations?