Physics 325 Spring 2011 Problem Session 7

# Physics 325 Spring 2011 Problem Session 7 - x t = x p t B...

This preview shows page 1. Sign up to view the full content.

Physics 325 Spring 2011 Discussion 7 March 14, 2011 Consider an overdamped driven harmonic oscillator with driving force proportional to e - σt , for some constant σ > 0 . The equation of motion is therefore ¨ x + 2 β ˙ x + ω 2 0 x = F e - σt . (a) Find a particular solution of this differential equation. (b) Let e - λ 1 t and e - λ 2 t be the homogeneous solutions. Determine λ 1 and λ 2 in terms of β and ω 0 . (c) Suppose the initial conditions are such that the full solution is
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x ( t ) = x p ( t ) + B e-Î» 1 t + C e-Î» 2 t , where B and C are not zero. Here, x p ( t ) is the particular solution from part (a). If Ïƒ < Î» 1 and Ïƒ < Î» 2 , what is the behavior of x ( t ) as t â†’ âˆž ? (d) Assume F is positive. For what range of Ïƒ will x p ( t ) be negative?...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business â€˜17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. Itâ€™s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania â€˜17, Course Hero Intern

• The ability to access any universityâ€™s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLAâ€™s materials to help me move forward and get everything together on time.

Jill Tulane University â€˜16, Course Hero Intern