unit 6 lesson 2 mass on a spring and pendulums mass spring system - energy

Unit 6 Lesson 2 Mass on a Spring and Pendulums

http://ia700200.us.archive.org/20/items/AP_Physics_C_Lesson_19/Container.htmlMass Spring System - Energy

HomeworkSERWAY Page 416: #’s 25, 29, 33

Page 416 #’s 23, 24, 26, 27, 28

Mass – Spring SystemVertical Spring Force vs. GravityHorizontal Spring Force vs. Friction

Work = ½ kx2

Net Work = ZeroKinetic Energy + Potential Energy = Total

½ mv2 + ½ kA2 = TEVelocity = √[{k/m}(A2 - x2 )]

Period T = 2π/ω T = 2π √[{m/k}]

Frequency f = 1/T = ω/2π = √[{k/m}]/ 2π Position x = A Cos{ωt}Angular Velocity ω = √[{k/m}] = 2π / TAcceleration α= – ω 2 x

http://www.youtube.com/watch?v=j-zczJXSxnwTacoma Narrows Bridge

http://ia600706.us.archive.org/7/items/AP_Physics_C_Lesson_20/Container.htmlPendulums

Simple PendulumA simple pendulum is one which can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency. For small amplitudes, the period of such a pendulum can be approximated by:

For small angles θ the solution is:

Physical Pendulum

Again for small angles < 15 degrees or .26 radians

Rod Pendulum

A physical pendulum in the form of a uniform rod suspended by its end has a period given by:

Note that the period is independent of the mass and radius of the rod.

http://www.learnapphysics.com/apphysicsc/oscillation.phpPractice Review Problems

Lab V-E14 Pendulum PeriodsLab Hooke’s Law - Kinematics