- #1

Yoonique

- 105

- 0

## Homework Statement

In the Cavendish experiment, the two small balls have mass m each and are connected by a light rigid rod with length L. The two large balls have mass M each and are separated by the same distance L. The torsion constant of the torsion wire is κ.

b) Put the large balls a small distance away from the small balls, when the system reaches the equilibrium, the rigid rod rotates an angle θ and the distance between the centers of balls is r, as shown in the above figure. Find the expression for the gravitational constant G.

c)If the small balls are perturbed with small angle from the equilibrium position in (b), will the oscillation be harmonic? If so, find the expression for the period of the oscillation.

## Homework Equations

∑τ = Iα

T = 2π/ω

## The Attempt at a Solution

I solved for part b. But I can't get the answer to part c.

Part b: G = 2π

^{2}Lr

^{2}θ/(MT

^{2})

Part c:

Let the new angle be θ

_{1}

∑τ = Iα

GMmL/(r-0.5θcosθ

_{1})

^{2}- κθ

_{1}= Iα

α = 2GM/(L(r-0.5θcosθ

_{1})

^{2}) - 2κθ

_{1}/(mL

^{2})

I can't make α=-ω

^{2}θ

_{1}to find for ω to solve for T.

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