Section 12­1.notebook
March 08, 2012
Simple Harmonic Motion ­ is vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium.
Examples are a pendulum or a spring.
As a pendulum swings back and forth, the maximum displacement the velocity of the pendulum is zero. Once it reaches back to center (equilibrium) the velocity reaches it maximum. The pendulum swings through and reaches maximum displacement on the other side (velocity is zero again). The pendulum repeats the process. At maximum displacement the spring force reaches its maximum acceleration.
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Section 12­1.notebook
March 08, 2012
In simple harmonic motion the restoring force is proportional to displacement.
Hooke's Law
Felastic = ­kx
spring force = ­(spring constant x displacement)
If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?
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Section 12­1.notebook
March 08, 2012
When a spring is stretched or compressed is has elastic potential energy. Example of a simple pendulum is like a swing. The basic form of pendulum is a bob attached to a fixed spring. The restoring force of a pendulum is a component of the bob's weight. If a pendulum's motion is simple harmonic the restoring force must be proportional to the displacement; then the pendulum's motion is simple harmonic. If the pendulum is placed on a coordinate system the y component at any one point will be the force exerted on the bob by the string and gravity. The x component is tangent to the direction of the motion of the ball. It is the net force of the bob's weight acting in the direction of its motion.
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Section 12­1.notebook
March 08, 2012
The pendulum's motion is simple harmonic for angles < 15. Total mechanic energy is still conserved in simple harmonic situations.
When a pendulum is in equilibrium; it has the least amount of gravitational potential energy (zero) and is solely kinetic energy. When the pendulum reaches its greatest displacement; the gravitational potential energy is the greatest and the kinetic energy is zero. During the entire movement of the pendulum the amount of kinetic and potential energy are changing, yet will still result in the same total mechanical energy. 4
Section 12­1.notebook
March 08, 2012
Simple Harmonic Motion
Fx = Fmax a = amax v = 0
maximum displacement
θ
equilibrium
Fx = 0
maximum displacement
Fx = Fmax a = amax v = 0
a = 0
v = vmax
θ
equilibrium
Fx = 0
a = 0
v = vmax
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Section 12­1.notebook
March 08, 2012
Practice 12A ­ all
Section 12­1 Review ­ all
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