1 / 24

Simple Harmonic Motion

Simple Harmonic Motion. AP Physics C Mrs. Coyle. Periodic Motion. A motion of an object that repeats with a constant period. http://www.sccs.swarthmore.edu/users/08/ajb/e71/lab1/. Simple Harmonic Motion. It is a periodic motion. AND

patriciafranklin
Download Presentation

Simple Harmonic Motion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Simple Harmonic Motion AP Physics CMrs. Coyle

  2. Periodic Motion • A motion of an object that repeats with a constant period. http://www.sccs.swarthmore.edu/users/08/ajb/e71/lab1/

  3. SimpleHarmonicMotion • It is aperiodic motion. AND • It has a restoringforce thatacts to restore the oscillator to equilibrium. The restoring force is given by: Hooke’s Law F=-kx x is the displacement from equilibrium and k is the force constant (spring constant). • The period of SHM oscillator does not depend on the amplitude.

  4. Simple Harmonic Motion Simulations http://bcs.wiley.com/he-bcs/Books?action=mininav&bcsId=3606&itemId=0471758019&assetId=111700&resourceId=10211 -SHM -Particle oscillating in SHM

  5. Calculating k from a F vs x Graph • k is the slope of a F vs x graph

  6. Remember: • For springs in series: 1/keff = 1/k1 + 1/k2 • For springs in parallel: keff = k1 + k2

  7. The acceleration in SHM is not constant:

  8. Acceleration in Simple Harmonic Motion • Acceleration • Let • a = -w2x

  9. Characteristic Quantities of Simple Harmonic Motion • Displacement • Amplitude: maximum displacement • Frequency • Period • f=1/T T=1/f

  10. SimpleHarmonicMotion • Velocity: • maximum as it passes through equilibrium • zero as it passes through the extreme positions in its oscillation. • Acceleration: a=F/m = -kx/m -maximum at extreme points -zero at equilibrium

  11. Equations of Motion-Displacement • x=Asin(wt +f) or x=Acos(wt +f) • x=-Asin(wt +f) x=-Acos(wt +f) • w=angular frequency, rad/s • f is the phase constant

  12. Example x • What is the amplitude? • What is the period? • c) What total distance does the particle travel in one period?

  13. Example x Write the equation of motion for the above oscillator. Answer: x=-0.5sin(πt)

  14. Note • The acceleration is not constant and therefore the kinematics equations cannot be used.There are two options: • Use conservation of mechanical energy to find v at a given position. E= ½ mv2 + ½ kx2 = constant or 2. Take the first derivative of x (equation of motion) to find v and the second derivative to find a.

  15. Remember

  16. Examples of Motion Equations for Simple Harmonic Motion

  17. The velocity is 90o out of phase with the displacement The acceleration is 180o out of phase with the displacement Graphs of SHM

  18. Example 1 • t = 0 x (0)= A v (0) = 0 • f= 0 • amax =± w2A vmax = ± wA

  19. Example 2 • t = 0 x (0)=0 v (0) = vi f = - p/2 • The graph is shifted one-quarter cycle to the right compared to the graph of x (0) = A

  20. Period and Frequency

  21. Period of A Spring Mass Oscillator ____ • T=2p√m/k • m mass • k spring constant • T does not depend on g • The period is smaller for a stiffer spring (large values of k).

  22. Harmonic Motion of a Pendulum • http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true • Period ___ T=2p√L/g • L=length of string • T depends on g L

  23. Question • If you had a spring-mass system on the moon, would the period be the same or different than that of this system on the earth? • What if it were a pendulum system?

More Related