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Simple Harmonic Motion

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Simple Harmonic Motion & Elasticity Chapter 10 Elastic Potential Energy What is it? Energy that is in materials as a result of their . Where is it found? – PowerPoint PPT presentation

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Title: Simple Harmonic Motion


1
Simple Harmonic Motion Elasticity
  • Chapter 10

2
Elastic Potential Energy
  • What is it?
  • Energy that is in materials as a result of
    their .
  • Where is it found?

3
Law
  • A spring can be or with a .
  • The by which a spring is compressed or
    stretched is to the magnitude of the
    ( ).
  • Hookes Law
  • Felastic
  • Where
  • spring constant of spring ( )
  • displacement

4
Hookes Law
  • What is the graphical relationship between the
    elastic spring force and displacement?
  • Felastic -kx

5
Hookes Law
  • A force acting on a spring, whether stretching or
    compressing, is always .
  • Since the spring would prefer to be in a
    relaxed position, a negative force will
    exist whenever it is deformed.
  • The force will always attempt to bring
    the spring and any object attached to it back to
    the position.
  • Hence, the restoring force is always .

6
Example 1
  • A 0.55 kg mass is attached to a vertical spring.
    If the spring is stretched 2.0 cm from its
    original position, what is the spring constant?
  • Known
  • m
  • x
  • g
  • Equations
  • Fnet (1)
  • (2)
  • (3)
  • Substituting 2 and 3 into 1 yields
  • k
  • k
  • k

7
Elastic in a Spring
  • The exerted to put a spring in tension or
    compression can be used to do . Hence the
    spring will have Elastic .
  • Analogous to kinetic energy

8
Example 2
  • What is the maximum value of elastic potential
    energy of the system when the spring is allowed
    to oscillate from its relaxed position with no
    weight on it?
  • A 0.55 kg mass is attached to a vertical spring
    with a spring constant of 270 N/m. If the spring
    is stretched 4.0 cm from its original position,
    what is the Elastic Potential Energy?
  • Known
  • m 0.55 kg
  • x -4.0 cm
  • k 270 N/m
  • g 9.81 m/s2
  • Equations
  • PEelastic
  • PEelastic
  • PEelastic

9
Elastic Potential Energy
  • What is area under the curve?

A A A A Which you should see equals the

10
Simple Harmonic Motion Springs
  • Simple Harmonic Motion
  • An around an will occur when an
    object is from its equilibrium position and
    .
  • For a spring, the restoring force F -kx.
  • The spring is at equilibrium
  • when it is at its relaxed length.
  • ( )
  • Otherwise, when in tension or
  • compression, a restoring
  • force exist.

11
Simple Harmonic Motion Springs
  • At displacement ( )
  • The Elastic Potential Energy will be at a
  • The force will be at a .
  • The acceleration will be at a .
  • At (x )
  • The Elastic Potential Energy will be
  • Velocity will be at a .
  • Kinetic Energy will be at a
  • The acceleration will be , as will the
    force.

12
10.3 Energy and Simple Harmonic Motion
Example 3 Changing the Mass of a Simple Harmonic
Oscilator
A 0.20-kg ball is attached to a vertical spring.
The spring constant is 28 N/m. When released
from rest, how far does the ball fall before
being brought to a momentary stop by the spring?
13
10.3 Energy and Simple Harmonic Motion
14
Simple Harmonic Motion of Springs
  • Oscillating systems such as that of a spring
    follow a pattern.
  • Harmonic Motion of Springs 1
  • Harmonic Motion of Springs (Concept Simulator)


15
Frequency of Oscillation
  • For a spring oscillating system, the frequency
    and period of oscillation can be represented by
    the following equations
  • Therefore, if the of the spring and the
    are known, we can find the and
    at which the spring will oscillate.
  • k and mass equals frequency of
    oscillation (A spring).

16
Harmonic Motion The Simple Pendulum
  • Simple Pendulum Consists of a massive object
    called a suspended by a string.
  • Like a spring, pendulums go through
  • as follows.
  • Where
  • Note
  • This formula is true for only of .
  • The period of a pendulum is of its mass.

17
Conservation of ME The Pendulum
  • In a pendulum, is converted into
    and vise-versa in a continuous repeating pattern.
  • PE mgh
  • KE ½ mv2
  • MET PE KE
  • MET
  • Note
  • kinetic energy is achieved at the point of
    the pendulum swing.
  • The potential energy is achieved at the
    of the swing.
  • When is , , and when
    is , .

18
Key Ideas
  • Elastic Potential Energy is the in a spring
    or other elastic material.
  • Hookes Law The of a spring from its
    is the applied.
  • The of a vs. is equal to the
    .
  • The under a vs. is equal to the
    done to compress or stretch a spring.

19
Key Ideas
  • Springs and pendulums will go through oscillatory
    motion when from an position.
  • The of of a simple pendulum is of
    its of displacement (small angles) and .
  • Conservation of energy Energy can be converted
    from one form to another, but it is
    .
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