Numerical Solution to the Single Degree of Freedom (SDOF) Problem - Part 1 - Mathematical Derivation

A method of finding approximate, numerical solutions for the simple harmonic oscillator with damping. A mathematical description of a time-stepping solution used to solve the equation of motion for the single-degree-of-freedom (SDOF) problem.

[Chemasaurus]

You sir, just earned yourself +1 to your subscriber count. Well done

[MartinWalter]

The way of your explanation is great. Thanks!

[AJ-etvf]

Cool lecture as usual. And I'm overjoyed when you said that you'll implement the code in Python. I've been interested in relearning Python to aid me in numerical analysis and I definitely appreciate this!.

[keoagilekerileng]

Awesome Lecturer, awesome information, I am now gaining. very very hopeful. Thanks alot. I will watch all the playlist and try answer my problem challenges right in front of me.

[krzysztofk]

Hello @Good Vibrations with Freeball, Your videos are SUPERB!
However I have a dumb question. At 2:14 you start to rewrite everything in matrices. I am stuck at that moment. Could you please explain step by step from where exactly you get these coefficients {m, 0} {c, k} {f(t)} then in new line {0, 1}, {-1, 0} and {0}?

[r.a]

Hi. Thank you. Please did make any videos that dealt directly with using Newmark's method to solve examples of free undamped vibrations?

[joaopedromacedofernandes]

great! I am curious to know how to equate numerically in problems with coulomb friction

[dhk]

Very easy to understand. I appreciate it.

[jake]

Hello there, great video. I was wondering what you call this method of finding the numerical solution? Is it simply just called a time stepping solution or does it have a name such as RK4 or Newmark's method?

[aliyyekara]

Excellent lecture. Very-well explained. I hope that there will be a lecture series for vibration of continous systems.

[arpitsharma]

in your total energy consistency equation why there is no mention of energy being dissipated in the damper

[cobbysparks]

You should banned for being this good. 😅. Good stuff sir. Subscribed, Following. Notifications turned on. Thank you!

[chinocapuchino]

Mr could you make a video explaining the modeling of a rotational system by euler-lagrange? Thks!

[alexsandercosta]

Hi Freeball! Your videos are awesome and that's also the reason I went here to ask you something about state space equations. I have the following equation: r'' = - GM/r² (from Newton's law of universal gravitation). I'd like to know what's the state-space form of this equation and how I can implement this on Python using the A and B matrices like you used for this problem in this video..
Thanks in advance!

[Hudmyq]

Hi，Freeball, your video is very helpful. Could you please do some videos about cable vibration?