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Chapter 11: Section 1

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Chapter 11: Section 1 Simple Harmonic Motion (SHM) Periodic Motion A repeated motion that moves back and forth over the same path. Examples include: pendulum ... – PowerPoint PPT presentation

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Title: Chapter 11: Section 1


1
Chapter 11 Section 1
  • Simple Harmonic Motion (SHM)

2
Periodic Motion
  • A repeated motion that moves back and forth over
    the same path.
  • Examples include pendulum, vibrating string,
    orbiting planet

3
Simple Harmonic Motion (SHM)
  • A special kind of periodic motion
  • Results from a restoring force that is
    proportional to displacement.
  • Restoring Force force that tries to reestablish
    equilibrium.
  • During SHM, an object oscillates (vibrates back
    and forth) around a central equilibrium position.

4
Springs stretching
0
  • When you stretch a spring, you must apply an
    increasing amount of force as the displacement
    increases.
  • That means the spring is pulling back with an
    equal and opposite force

5
Springs compressing
0
  • When you compress a spring, you must apply an
    increasing amount of force as the displacement
    increases.
  • That means the spring is pushing back with an
    equal and opposite force

6
  • Displaced Position
  • -Force is at maximum
  • -Since Fma a max
  • -v 0
  • Equilibrium Position
  • -Net Force 0
  • -Since Fma a 0
  • -v maximum

7
Hooks Law
  • Felastic - k ? x
  • K Spring Constant (measures stiffness of
    spring)
  • ? x displacement from equilibirum)
  • - sign indicates that the force is opposite
    displacement

8
  • A stretched or compressed spring has elastic
    potential energy.
  • Work needed to stretch or compress a string
  • W½ k?x2
  • Since work change in PE
  • PE ½ k?x2
  • Taking various forms of energy into account, the
    total energy is given by
  • E ½ mv2 mgh ½ k?x2

9
Sample Problem
  • If a mass of 0.25 kg attached to a vertical
    spring stretches the spring 3.0 cm from its
    equilibrium position, what is the spring constant?

10
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11
Sample problem
  • A 1.80 kg object is connected to a spring of
    force constant 120 N/m. How far is the spring
    stretched if it is used to drag the object across
    a floor at constant velocity? Assume the
    coefficient of kinetic friction is 0.60.

12
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13
A Simple Pendulum
  • Consists of a mass, called a bob
  • The restoring force of a pendulum is a component
    of the bobs weight.
  • When the angle is lt15 degrees, the restoring
    force is proportional to the displacement.
  • For small angles, the pendulums motion is
    simple harmonic.

14
A Simple Pendulum Cont.
  • Please note FT tension force, F r restoring
    force and U is another symbol for Potential
    Energy
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