Navigating Damped and Forced Harmonic Motion

[Saoist]

hi guys,

doing damped and forced harmonic motion at college at the moment, but i don't do further maths...hence I'm a tad behind compared to those who do (half the class). we don't need to know it for the exam itself, but you know...curiosity. does anyone know of any good online resources about FHM and DHM, maths included, but which explains clearly and concisely?

one major problem i have is that I've never seen the result:

e^(ipt)=cos(pt)+isin(pt) before. saw this in the middle of the DHM derivation which we were shown for all of 30seconds, scribbled it down.does anyone have a good derivation for this please?

 

[DeadWolfe]

Actually it's the definition of the complex exponential.

But to see that it makes sense, simple plug ipt into the power series of e^x, and look at what you get.

 

[sir-pinski]

Hi there! I can definitely relate to feeling behind in a class, especially when it comes to math. Damped and forced harmonic motion can definitely be a tricky subject, but there are definitely some great online resources that can help you understand it better.

First of all, I would recommend checking out Khan Academy's videos on damped and forced harmonic motion. They have a whole series of videos on the topic that break down the concepts and equations in a clear and concise way. They also have practice problems and quizzes to help you test your understanding.

Another great resource is the MIT OpenCourseWare website, which offers free online courses from MIT. They have a course specifically on damped and forced harmonic motion that includes lecture notes, practice problems, and even video lectures. It might be a bit more advanced, but it could definitely help you understand the topic in more depth.

As for the derivation of e^(ipt)=cos(pt)+isin(pt), I would recommend checking out Paul's Online Math Notes. They have a section specifically on complex numbers and trigonometry, which includes a derivation of this formula. They also have practice problems and examples to help solidify your understanding.

I hope these resources help you out! Just remember to take your time and practice as much as you can. With a bit of effort and persistence, I'm sure you'll be able to catch up and excel in this subject. Best of luck!