Recent content by horserider37

I got it! Thanks yall! I do *know* calculus, but I'm really bad with symbols and always overthink. I was severely complicating my derivatives lol, trying to make them much harder than they needed to be. Switching to a,b,c did the trick!

My algebra/calculus is horrible, hence the issue I think! I still don't understand how to find what minimizes that

I'm not sure what you mean by that. Like $$\omega_d<\omega_0$$ even as ##\omega_d## varies?

When the denominator is smallest, right?. But how do I go from that to that formula?

$$A(\omega_d)=\frac{F/m}{\sqrt{(\omega_0^2-\omega_d^2)^2+(\frac{\omega_0}{Q}\omega_d)^2 }}.$$ I think that's right. There was a missing square in your eqn. No, I can't tell. Should I be able to? I feel like I'm missing something stupidly easy.

It's part of a textbook problem. It's damped and driven harmonic oscillators - there's lots of equations but I think the relevant ones are x''+γx'+(w0^2)x=F/m(cos(wdt)) and amplitude = A(wd)=(F/m)/√(((w0^2-wd^2)^2)+((γwd)^2)) but maybe there's others? I just confused in general. I don't know...

Hi everyone, I'm stuck on how to show the peak of the amplitude resonance curve is at wd = w0√(1-1/2Q^2), where Q = w0/γ. My first instinct is to take a derivative of something and set = 0, but what eqn?Help?