Simple Harmonic Motion Question Watch

MEPS1996
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Why does the time period of an object in SHM, not depend on the amplitude?
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HandmadeTurnip
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(Original post by MEPS1996)
Why does the time period of an object in SHM, not depend on the amplitude?
Because they're completely independent of each other. Imagine two pendulums that swing the same distance but one swings twice as quickly as the other. They both have the same amplitude (maximum displacement) but different periods (how quickly they swing).
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RoyalBlue7
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You could deduce that from the equations of motion for the SHM.

Theoretically every SH system has a natural frequency and hence a time period for free oscillations

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ChrissM
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(Original post by HandmadeTurnip)
Because they're completely independent of each other. Imagine two pendulums that swing the same distance but one swings twice as quickly as the other. They both have the same amplitude (maximum displacement) but different periods (how quickly they swing).
The only way they could swing the same distance (they would have to have equal lengths), and have the same amplitude, but have different time periods is if the gravitational field strength acting on each pendulum was different. The analogy you used is slightly confusing and doesn't really answer the question.

To the OP, it's because the motion has a natural frequency (depending on the mass and the spring constant, k), so the amplitude isn't going to affect this natural frequency, thus the time period isn't affected by the amplitude.
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Stonebridge
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(Original post by MEPS1996)
Why does the time period of an object in SHM, not depend on the amplitude?
When you ask "why" in physics you only get an answer which refers you to something else. In this case it's in the maths.
Do the maths for the period of a pendulum or a mass on a spring and the amplitude is not a term in the answer. It "cancels". There's no other way to show exactly why.

Intuitively, when you increase the amplitude, you increase the restoring force (it is proportional to displacement from equilibrium).
If you increase the restoring force you increase the acceleration of the mass and hence its speed. Increasing its speed would normally shorten the time it takes for one oscillation, but by increasing the amplitude you have given it further to go.
The two effects just happen to cancel.
Why? See the maths.
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MEPS1996
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(Original post by Stonebridge)
When you ask "why" in physics you only get an answer which refers you to something else. In this case it's in the maths.
Do the maths for the period of a pendulum or a mass on a spring and the amplitude is not a term in the answer. It "cancels". There's no other way to show exactly why.

Intuitively, when you increase the amplitude, you increase the restoring force (it is proportional to displacement from equilibrium).
If you increase the restoring force you increase the acceleration of the mass and hence its speed. Increasing its speed would normally shorten the time it takes for one oscillation, but by increasing the amplitude you have given it further to go.
The two effects just happen to cancel.
Why? See the maths.
i can see that the derivation of time period for both a mass on a spring a simple pendulum are both independent of amplitude. I was just looking for something more general, something innate to SHM that means they are independent.
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Stonebridge
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(Original post by MEPS1996)
i can see that the derivation of time period for both a mass on a spring a simple pendulum are both independent of amplitude. I was just looking for something more general, something innate to SHM that means they are independent.
It's innate in the mathematics. Once you define SHM in the way you do, it's a natural consequence.
To return to what I said in my 1st post.

If you had to travel a distance s, starting from rest, with an acceleration a, the time taken would by given by s = ½at²

the time taken would be

\sqrt\frac{2s}{a}}

If, for some reason, we were to stipulate that the acceleration is proportional to the distance you need to travel (a = ks in the above) then the time would be independent of s as it would cancel top and bottom.
This is in effect what you are doing with SHM, though it's a little more complicated, as the acceleration is changing, but it still works with the concept of average acceleration.
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