SIMPLE HARMONIC MOTION

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SIMPLE HARMONIC MOTION
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STARTER

• MAKE A LIST OF OBJECTS THAT EXPERIENCE VIBRATIONS

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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.

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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

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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

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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.

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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

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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

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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

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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

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DEFINITION

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