Simple%20Harmonic%20Motion

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Simple Harmonic Motion

• Physics
• Ms. Shaver

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(No Transcript)
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Periodic Motion
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Simple Harmonic Motion

• Is a periodic motion that repeats at constant
  frequency.
• Has a restoring force that acts to restore the
  oscillator to equilibrium.
• F-kx Hookes Law
• x displacement from equilibrium
• k spring
• constant

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Characteristic Quantities of Simple Harmonic
Motion

• Displacement distance from equilibrium.
• Amplitude maximum displacement

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Characteristic Quantities of Simple Harmonic
Motion

• Frequency oscillations per unit time
• Unit 1/sec Hertz
• Period time to complete one oscillation
• Unit sec
• f1/T T1/f

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Simple Harmonic Motion

• Velocity
• maximum as it passes through equilibrium
• zero as it passes through the extreme positions
  in its oscillation.
• Acceleration aF/m -kx/m
• -maximum at extreme points
• -zero at equilibrium

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Mass on a Spring

• Applet
• http//www.walter-fendt.de/ph14e/springpendulum.ht
  m

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Position vs Time Graph of Mass on Spring(Sine
Curve)
x

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

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Period of A Spring Mass Oscillator

• ____
• T2pvm/k
• T period (s)
• m mass (kg)
• k spring constant (N/m)

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Problem

• Calculate the period of a mass of 5kg on a spring
  that has a spring constant of 20N/m.
• Answer 3s

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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?

NO. mass and spring constant do not depend on
gravity.
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Solve for m or k
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Harmonic Motion of a Pendulum

• Applets
• http//www.walter-fendt.de/ph14e/pendulum.htm
• http//www3.interscience.wiley.com8100/legacy/co
  llege/halliday/0471320005/simulations6e/index.htm?
  newwindowtrue

L
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Harmonic Motion of a Pendulum

• http//www3.interscience.wiley.com8100/legacy/col
  lege/halliday/0471320005/simulations6e/index.htm?n
  ewwindowtrue
• Period
• ___
• T2pvL/g
• g9.8m/s2
• Llength of string

L
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Problem

• Calculate the Period of a pendulum of length 0.75
  m.Answer 1.7s

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Question

• If you had a pendulum on the moon would its
  period be the same or different compared to the
  same pendulum on the earth?

Different because the period depends on gravity,
which on the moon is 1.62 m/s2
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Solving for g or L
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Questions

• Does the period of a pendulum depend on the mass
  of the bob?
• If you increase the length of the pendulum
  string, what happens to the period?

NO. There is no m in the equation.
It will increase by the square root of L.
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Calculating k from a F vs x Graph

• k is the slope of a
• F vs x graph

F -kx Y mx b
Slope rise/run 100 N/5 m 20 N/m