Error Propagation: Dividing By 20 in Pendulum Timing

In summary, the conversation discusses the measurement of time for 20 oscillations of a pendulum and the relationship between the period T and the measured time t. It is explained that when dividing by 20, the required answer is obtained, and this is due to the fact that the numerical value of 20 does not affect the error propagation. The conversation also highlights the concept of error ΔT and its relationship with the true period.
  • #1
PhysicStud01
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Homework Statement


suppose i measure the time t for 20 oscillations fro a pendulum. the period is T.

Homework Equations


Since T = t / 20
delta T = delta t right?

The Attempt at a Solution


since the 20 is a numerical value, it does not come in the error propagation, does not? when i used the above equation, i can't get the required answer but when i divide by 20, the answer is obtained.

can someone explain why?
 
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  • #2
T is what you measure the period to be, right? (T = t / 20) So the true period will be T+ΔT where ΔT is some error.

The true time it takes for 20 oscillations is 20(T+ΔT), which equals the time you measured plus some error Δt

[itex]20(T+ΔT)=t+Δt[/itex]

So if [itex]20T=t[/itex] then:

[itex]20ΔT=Δt[/itex] ... or ... [itex]ΔT=\frac{Δt}{20}[/itex]
 

1. How does dividing by 20 affect the accuracy of pendulum timing measurements?

Dividing by 20 in pendulum timing involves dividing the total time measurement by 20 to account for the number of swings that occur in a single timing cycle. This affects the accuracy by reducing the overall time measurement and therefore increasing the precision of the timing.

2. Why is dividing by 20 necessary in pendulum timing?

Dividing by 20 is necessary in pendulum timing because it accounts for the number of swings that occur in a single timing cycle. This allows for a more precise measurement of time as it eliminates the extra swings and focuses on the exact timing cycle.

3. What are the potential sources of error when dividing by 20 in pendulum timing?

Potential sources of error when dividing by 20 in pendulum timing include human error in counting the number of swings, inconsistencies in the pendulum's swing pattern, and external factors such as air resistance or gravitational pull.

4. How can one minimize error when dividing by 20 in pendulum timing?

To minimize error when dividing by 20 in pendulum timing, it is important to have precise and consistent counting of the number of swings, as well as ensuring the pendulum has a consistent swing pattern. Additionally, conducting multiple trials and taking the average of the measurements can help reduce the impact of any potential errors.

5. Are there any alternative methods to dividing by 20 in pendulum timing?

Yes, there are alternative methods to dividing by 20 in pendulum timing. One method is to measure the time for a larger number of swings, such as 50 or 100, and then dividing by the corresponding number of swings. Another method is to use a more precise timing instrument, such as a digital stopwatch, to eliminate the need for dividing by 20.

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