Lecture 20: Ideal Spring and Simple Harmonic Motion

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Lecture 20 Ideal Spring and Simple Harmonic
Motion

• New Material Textbook Chapters 10.1 and 10.2

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Ideal Springs

• Hookes Law The force exerted by a spring is
  proportional to the distance the spring is
  stretched or compressed from its relaxed
  position.
• FX -k x Where x is the displacement from
  the relaxed position and k is the constant
  of proportionality. (often called spring
  constant)

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Ideal Springs

• Hookes Law The force exerted by a spring is
  proportional to the distance the spring is
  stretched or compressed from its relaxed
  position.
• FX -k x Where x is the displacement from
  the relaxed position and k is the constant
  of proportionality. (often called spring
  constant)

relaxed position
FX -kx gt 0
x
x ? 0
x0
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Ideal Springs

• Hookes Law The force exerted by a spring is
  proportional to the distance the spring is
  stretched or compressed from its relaxed
  position.
• FX -k x Where x is the displacement from
  the relaxed position and k is the constant
  of proportionality. (often called spring
  constant)

relaxed position
FX - kx lt 0
x
x gt 0
x0
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Concept Question

• In Case 1 two people pull on the same end of a
  spring whose other end is attached to a wall. In
  Case 2, the same two people pull with the same
  forces, but this time on opposite ends of the
  spring. In which case does the spring stretch the
  most?
• 1. Case 12. Case 23. Same

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What does moving along a circular path have to do
with moving back forth in a straight line
(oscillation about equilibrium) ??
x
8
8
q
R
7
7
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Concept Question

• A mass on a spring oscillates back forth with
  simple harmonic motion of amplitude A. A plot of
  displacement (x) versus time (t) is shown below.
  At what points during its oscillation is the
  speed of the block biggest?
• 1. When x A or -A (i.e. maximum displacement)
• 2. When x 0 (i.e. zero displacement)
• 3. The speed of the mass is constant

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Concept Question

• A mass on a spring oscillates back forth with
  simple harmonic motion of amplitude A. A plot of
  displacement (x) versus time (t) is shown below.
  At what points during its oscillation is the
  magnitude of the acceleration of the block
  biggest?
• 1. When x A or -A (i.e. maximum displacement)
• 2. When x 0 (i.e. zero displacement)
• 3. The acceleration of the mass is constant

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Springs and Simple Harmonic Motion
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Simple Harmonic Motion
x(t) Acos(?t) v(t) -A?sin(?t) a(t)
-A?2cos(?t)
x(t) Asin(?t) v(t) A?cos(?t) a(t)
-A?2sin(?t)
OR
Period T (seconds per cycle) Frequency f
1/T (cycles per second) Angular frequency ?
2?f 2?/T For spring ?2 k/m
xmax A vmax A? amax A?2