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SIMPLE HARMONIC MOTION

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SIMPLE HARMONIC MOTION STARTER MAKE A LIST OF OBJECTS THAT EXPERIENCE VIBRATIONS: PERIODIC MOTION PERIODIC MOTION: Any motion that repeats itself precisely over equal ... – PowerPoint PPT presentation

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Title: SIMPLE HARMONIC MOTION


1
SIMPLE HARMONIC MOTION
2
STARTER
  • MAKE A LIST OF OBJECTS THAT EXPERIENCE VIBRATIONS

3
PERIODIC MOTION
  • PERIODIC MOTION Any motion that repeats itself
    precisely over equal periods of time.
  • If that periodic motion is generated by a linear
    restoring force it is SIMPLE HARMONIC MOTION.

4
HOOKEs LAW
  • Recall Hookes Law
  • F -kx
  • x is the amount of extension or compression of a
    spring
  • Spring constant, k , describes the force
    necessary to stretch or compress an individual
    spring. Each spring is different.
  • the negative sign indicates that the force always
    opposes the direction of the stretch, restoring
    the object to its rest or equilibrium position

5
Quantities that Describe Periodic Motion
  • Period the length of time required to complete
    one full cycle of motion
  • Frequency the number of cycles in a given time
  • Period and frequency are inversely related

6
ENERGY
  • ET ½ mv2 ½ kx2
  • x is the position
  • At the ends of the oscillation the mass stops and
    changes direction, so all of the energy is
    elastic potential energy
  • At equilibrium (x0) the string is not stretched
    so all energy is kinetic.

7
VELOCITY
  • v vmax v 1- x2/A2
  • v is the speed of the mass at any position of its
    motion
  • x is any position
  • A is maximum amplitude
  • vmax is the maximum speed occurs at equilibrium
    position

8
UNIFORM CIRCULAR MOTION
  • The amplitude of SHM is equal to the radius of
    Uniform Circular Motion
  • Use the UCM equations to describe SHM
  • a 4p2A/T2
  • vmax 2pA/ T Or T 2pA/ vmax

9
PERIOD and FREQUENCY of mass on spring
  • Another arrangement for vmax
  • vmax2 k/m A2
  • Substituting into UCM equation
  • T 2pvm/k
  • Equation for frequency
  • f 1/2p vk/m

10
PENDULUM
  • T 2p v l /g
  • l is the length of the pendulum string
  • g is acceleration due to gravity
  • This equation is valid for the period of a
    pendulum for small angles

11
DEFINITION
  • Simple Harmonic Motion a periodic vibratory
    motion in which the force is directly
    proportional to the displacement
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