Chapter 12 – Vibrations and Waves
12-1 Simple Harmonic Motion
Definitions to Recall:
Acceleration – the rate of change of velocity
Velocity – the time it takes to change a position; need motion and direction (no the same
as speed)
At the equilibrium position, velocity reaches a maximum and acceleration becomes
zero.
Demonstration with blocks and springs
I.
Pulling Mass Away (Max Displacement)
Explanation:_____________________________________________________________
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Spring force is to the ___________________.
Velocity is ______________________.
Acceleration will ________________________.
At maximum displacement, spring force and acceleration reach a maximum.
Demonstration with blocks and springs
II.
Spring Is Unstretched (Equilibrium)
Explanation:_____________________________________________________________
________________________________________________________________________
________________________________________________________________________
Spring force is to the ___________________.
Velocity is ______________________.
Acceleration will ________________________.
III.
Spring Is Compressed (Maximum Displacement)
Explanation:_____________________________________________________________
________________________________________________________________________
________________________________________________________________________
Spring force is to the ___________________.
Velocity is ______________________.
Acceleration will ________________________.
The spring force acting to the right causes the mass to change its direction, and the mass
begins moving back toward the equilibrium position. Then, the entire process begins
again, and the mass continues to oscillate back and forth over the same path.
**In an ideal system, the mass-spring system would oscillate indefinitely but, friction
comes into play.**
In simple harmonic motion, restoring force is proportional to displacement.
Restoring Force – spring force always pushes or pulls the mass back toward its
equilibrium position.
Simple Harmonic Motion – restoring force is directly proportional to the
displacement of the mass.
Robert Hooke found that most mass-spring systems obey a simple relationship between
force and displacement.
Hooke’s Law
Felastic = - kx
(spring force) = - (spring force X displacement)
--A negative sign shows that the spring force will tend to move the object back to its
equilibrium position.
--k = spring constant
What would a greater k mean in an experiment?
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Conceptual Challenge p.439