{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 5 - Lecture 5 SHM Pendulum Damping and Resonance Ch...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
April 15, 2008 Physics 40B Lecture 5 1 Review: Simple Harmonic Motion (SHM) of Mass-Spring System Hooke' s Law F s = ! kx U s = 1 2 kx 2 " = k m d 2 x dt 2 + 2 x = 0 (differential equation) Solution: x = A cos( t + # ) $ T = 2 % = 2 m k and f = 1 T = 1 2 k m v = dx dt v max = A a = dv dt = !" 2 x a max = 2 A Initial Conditions: x = x o , v = v o at t = 0 tan ! = " v o x o A = x o 2 + v o $ % & 2 Lecture 5 SHM: Pendulum, Damping and Resonance Ch. 13:5-8 Same equations for vertical oscillations with mass & spring. Use k = mg/ Δ L for spring constant where L is initial displacement in quilibrium positon due to mass.
Background image of page 1

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

View Full Document Right Arrow Icon
April 15, 2008 Physics 40B Lecture 5 2 Energy of Mass/Spring in SHM E = K + U = 1 2 mv 2 + 1 2 kx 2 E = 1 2 m ! A sin( t + " ) ( ) 2 + 1 2 k A cos( t + ) ( ) 2 Substituting 2 = k m E = 1 2 kA 2 is constant K = 1 2 m A sin( t + ) ( ) 2 = E sin 2 t + ( ) and U = E cos 2 t + ( ) K = E # U = 2 # 1 2 2 = 1 2 mv 2 $ v = ± k m 2 # x 2 ( ) Review: Energy of Mass/Spring System
Background image of page 2
April 15, 2008 Physics 40B Lecture 5 3 Simple Pendulum UCR Physics Foucault Pendulum: L~25 ft~8 m T = 2 π (8/9.8) 1/2 =5.7 s " = I #$" = % mg sin( & ) L Use small angle approx.
Background image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 10

Lecture 5 - Lecture 5 SHM Pendulum Damping and Resonance Ch...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online