Pendulum of unknown length and unknown g, only period given

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Homework Help Overview

The problem involves a pendulum with an unknown length and gravitational acceleration, given only the period of oscillation. The original poster states that the period is 9.32 seconds, and after increasing the length by 1 meter, the period changes to 9.734 seconds. The task is to find both the original length and the gravitational acceleration.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss expressing the period of the pendulum as a function of gravitational acceleration and length, suggesting that two equations can be formed from the two different lengths and periods.

Discussion Status

Some participants have confirmed the approach of using the period formula to create equations based on the two scenarios presented. There is a focus on the relationship between the variables involved, but no consensus has been reached on the specific values or methods to solve for the unknowns.

Contextual Notes

The problem does not assume a standard value for gravitational acceleration, which is a key aspect of the discussion. Participants are navigating the implications of this assumption in their reasoning.

mh1985
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Homework Statement



Pendulum of unknown length, l, has period of 9.32 seconds. Length is increased by 1 metre, and time period increases to 9.734 seconds. Calculate original length of pendulum and determine whether the experiment was conducted on earth. Hint: g is not assumed to be 9.81 ms^-2, you must find both g & l

Homework Equations



x(t) = A1 cos vnt + A2 sin vnt?

The Attempt at a Solution



Really not sure where to start, due to the two unknowns!
 
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Can you express the period as function of g and l?
For both pendulum lengths, you get an equation, so you have two unknowns and two equations.
 
mfb said:
Can you express the period as function of g and l?
For both pendulum lengths, you get an equation, so you have two unknowns and two equations.

T=2pi(sqrt(l/g) ?
 
That is right, and it will help you.
 

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