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Defining relation:
 |
(11) |
 |
(12) |
Solution:
 |
(13) |
 |
(14) |
Amplitude:
Period:
 |
(16) |
Maximum Speed:
 |
(17) |
Mechanical energy:
 |
(18) |
Initial Conditions:
The amplitude and phase can be determined from the initial position, xa, and velocity, va, at any initial time t = ta:
 |
(19) |
 |
(20) |
Graph of solution:
Figure 8:
Position-time and velocity-time graphs for the SHO
 |
Next: The Physical Pendulum
Up: SIMPLE HARMONIC MOTION -
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gabor@theory.uwinnipeg.ca
2001-01-05