Recent content by captainemeric

Homework Statement Consider an underdamped harmonic oscillator (Q > 1/2) with a sinusoidal driving force Focos(ωdt). (a) (5 pts) By using differential calculus find ωd that maximizes the displacement amplitude. (b) (7 pts) By using differential calculus find ωd that maximizes the velocity...

Ok, so I finally figured out I can find the % of TE in relation to the % of A lost. Which I can also use to find b which I can then use to find Q. A=Ainital exp^bt/2m where A/Ainital will equal .85 then the only unknown is b. And TE goes as A^2 so if A is 85% then TE is .85^2 or ~72%

1/2ka^2. How do i find this without being given a?

At maximum displacement, the kinetic energy should be zero. Should I be able to solve for the potential energy? I am so confused as to how to approach this. I know I have been given enough info but I feel like I don't have enough to find any additional values.

Homework Statement The displacement amplitude of a lightly damped oscillator with m=0.250kg and k=6400N/m is observed to decrease by 15% in exactly five minutes a) Calculate the fraction (in%0 of the initial mechanical energy of the oscillator that has been converted to other forms of energy...

That makes sense. That will then give me a real and an imaginary result of which I take the real I believe. Also, I apologize for the typo on the first post.

Yes, a is a real constant and |a| < 1. sorry about that

Homework Statement Use complex exponentials to prove 1 + acos(theta) + a^2cos(2theta) + a^3cos(3theta)... = (1 - acos(theta))/(1 - 2acos(theta) + a^2) Homework Equations euler's e^itheta/2 +e^-itheta/2=2cos(2theta) The Attempt at a Solution a^(n)cos(ntheta) = e^nitheta =...