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This 2 page Study Guide was uploaded by Usman Qureshi on Wednesday November 18, 2015. The Study Guide belongs to a course at a university taught by a professor in Fall. Since its upload, it has received 17 views.
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Date Created: 11/18/15
3 Last Lecture 3Power Impulse Center of Mass 3Today gtSimple Harmonic Motion 3 Important Concepts 3The physics of the motion is in the mass and spring constant which determine the period of each oscillation 3The amplitude does not affect the period 3Energy oscillates between Kinetic and Potential 801 L Fall 2005 11172005 Important Reminders 3 Pset 8 due tomorrow 3Problem Solving session in class tomorrow 3MasteringPhysics due next Monday ONOTE Class grading guidelines clearly allow discussion of MasterPhysics problems but also clearly prohibit directly working together or copying the answers of others 3N0 Pset due next week 3 No formal tutoring sessions next week 801 L Fall 2005 11172005 Center of Mass Velocity a 1 a 3Defnition CM A471 2 l l 3Connection to momentum MT0T17CM 13TOT 380 if momentum is conserved the velocity of the center of mass is constant 801 L Fall 2005 11172005 Simple Harmonic Motion l 3 Start with Force equation Fsprmg ki 70 3 Define x axis along direction spring is stretched and put xO at the point the spring is unstretched 2 Fx 2 kx max md t2 dzx k 2 x dt m 380 what is the solution to the differential equation 801 L Fall 2005 11172005 Simple Harmonic Motion ll 3The answer is sine andor cosine function with three mathematically equivalent ways to write it x Acosat q x A sinat p x A cosat B sinat 3 In all cases A B and 1 are constants determined by the initial conditions k 300 is given by the physics a m 801 L Fall 2005 11172005 Simple Harmonic Motion lll 3Connections to the physical motion 3A is the amplitude the maximum displacement from zero 31 is an arbitrary constant that depends only on when you define tO no real connection to the nature of the motion 30 is angular frequency in radians per second a 1 k Frequency 1n cycles second f 2727 2727 m 1 2 Period time for one cycle T 7r 272 E f a k 801 L Fall 2005 11172005 VelocityAcceleration in SHM 3Also sinecosine functions x Acosat p Vx dx dt Aa sin60t P d a2 2 V t Aw2 COSMN P k a2x x m 3 Note that Maximum speed lval 2 Au 801 L Fall 2005 11172005 Energy in SHM 1 2 kA2 2 OSprIng PE PE Ekx 27coswt spring 1 m A0 2 3 Kinetic energy KE 2 amt2 SIMW 152 3 Total 2 2 EM KE PE coswl 2 mg sinat 2 002 kA2 2 2 kA2 i 2 EToml 7cosal 51nal 2 2 vaax 801 L Fall 2005 11172005
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