PHYS 422 Lecture 15 Forced Vibrations and Resonace I

# PHYS 422 Lecture 15 Forced Vibrations and Resonace I - d V...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: d V i b t i d Forced Vibrations and esonance I Resonance I Harmonic Forcing hy should we care about this topic Why should we care about this topic Tacoma Narrows Bridge – 1940 - 42 mph wind drives oscillations Harmonic Forcing k F cos ω t k m ω = 2 d x Newton II: 2 2 cos s m kx F t dt d x k x F t ω = − + = 2 cos m k x F t dt ω + = – note that there are two frequencies: ω , the natural frequency, and ω , the driving frequency – we can expect that the motion will be a superposition of ω and ω 0 – transient motion → steady-state motion ω ω + ω – let’s look at the steady-state motion Harmonic Forcing k 2 x F cos ω t k m ω = 2 cos d x m k x F t dt ω + = – focus on two cases ¡ ω << ω 0 ⇒ oscillates at ~ ω with A ~ F /k = F /m ω 2 ⇒ response controlled by the spring stiffness ¡ ω >> ω x rm dominated by m(d 2 /dt 2 term ⇒ kx term dominated by m(d x/dt ) term ⇒ response governed by the inertia of the system ⇒ small A oscillation out of phase with the driving force...
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 ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’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 ‘17, Course Hero Intern

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

Jill Tulane University ‘16, Course Hero Intern