Simple Harmonic Motion, Initial Displacement vs Initial Cond

AI Thread Summary
The discussion revolves around the confusion regarding initial displacement in simple harmonic motion, specifically why an object initially displaced by 6 inches has an initial condition of -1/2. It is clarified that the initial displacement is often expressed as a fraction of the peak-to-peak amplitude, which can lead to negative values indicating direction. The minus sign reflects the restoring force acting opposite to the displacement direction. Additionally, the conversation touches on the relationship between initial velocity and amplitude, suggesting that the amplitude can exceed the initial displacement if the object does not start from rest. Overall, the participants confirm the understanding of these concepts in the context of both imperial units and simple harmonic motion principles.
austrosam
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Hi everybody,

I'm writing an exploration on the mathematics of simple harmonic motion and I stumbled across something I fail to understand in one of my resources (http://tutorial.math.lamar.edu/Classes/DE/Vibrations.aspx). In the example the author uses toward the end of the resource, the object is initially displaced by 6 inches (don't ask me why he felt the need to use imperial units) but then, the initial condition for displacement given at t=0 is -1/2. Should it not be 6?

My guess is that one can simply set t=0 at any point during the oscillation and not in fact when the oscillation is started, but that still would not quite explain everything. Maybe I am just being very silly...

Many thanks for any advice!

Sam
 
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If you pull a pendulum to one side by 6" and let it go it will swing back and forth a total distance of 12". So the initial displacement is half the peak to peak amplitude. It sounds like they decided to use "fraction of peak to peak amplitude" as the unit of displacement rather than inches or meters.

The minus sign is probably because the restoring force is in the opposite direction to the displacement.
 
CWatters said:
If you pull a pendulum to one side by 6" and let it go it will swing back and forth a total distance of 12". So the initial displacement is half the peak to peak amplitude. It sounds like they decided to use "fraction of peak to peak amplitude" as the unit of displacement rather than inches or meters.

The minus sign is probably because the restoring force is in the opposite direction to the displacement.
Right, I guess that makes sense, though I must say it still seems a little odd, to me it would seem much more straightforward to use a value of 6 inches instead.

Many thanks anyway!

One more thing, I merely need quick confirmation I'm on the right track here. Later on, they calculated the amplitude which was slightly larger than the initial displacement. Is this because of the initial velocity, and the object not starting from rest?
 
I f the author is using imperial units then the lengths would be in feet - so 6 inches is 1/2 a foot. Then they would use g=32 ft/sec/sec.
 
bhillyard said:
I f the author is using imperial units then the lengths would be in feet - so 6 inches is 1/2 a foot. Then they would use g=32 ft/sec/sec.

Perfect! Thank you! I am totally unfamiliar with imperial units, I should have really checked that. Thanks!
 

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