Period of a Simple Pendulum with Varying Masses and Gravitational Forces

AI Thread Summary
The discussion focuses on deriving an alternative expression for the period T of a simple pendulum considering varying inertial and gravitational masses. The standard formula T=2π√(l/g) is modified by substituting g with the expression g=GMg(mg)/(R²mi). Participants express uncertainty about whether this substitution aligns with the problem's requirements. The conversation emphasizes the relationship between the pendulum's period and the gravitational forces acting on it. Ultimately, the derivation aims to incorporate the effects of both mass types and Earth's characteristics.
rbwang1225
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Homework Statement


The usual formula for the period T of a simple pendulum of length l is T=2\pi\sqrt{\frac{l}{g}} where g is the acceleration due to gravity. Denoting rhe inertial mass of the pendulum bob by m_{i} and its gravitational mass by m_{g}, derive an alternative expression for T in terms of these masses, the radius R of the Earth and its mass M_{g}.


Homework Equations





The Attempt at a Solution



I just replaced g as \frac{GM_{g} {m_{g}}}{R^{2}m_{i}}.
I don't know if this is what the author wants.
 
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That looks correct to me.
 

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