Gravitational Field Strength Calculations with a Pendulum

[matt_crouch]

As a pendulum can be used to calculate the gravitational field strength by using the equation


Time period= 2(pi) sqrt (length/g)

this equation assumes that the pendulum bob is moving in Simple harmonic motion. However at very small lengths the pendulum bob tends to move in a more circular motion will this at all effect the time period and hense my value for g?

hopefully that makes sense =]
cheers

 

[ZapperZ]

It doesn't make sense, at least for me, because if you all you care about is to find "g", then why even make the length that small that it causes such circular motion?

And no, if you want it to be accurate, such circular motion can only add more systematic error to your estimation of g. Note that the formula for the period that you wrote assumes important simplifications: that the motion is a plane pendulum (not a 3D conical pendulum), and that it undergoes small oscillations, meaning a long pendulum with a small angle of oscillation. The more you deviate from that, the less accurate that period expression becomes.

Zz.

 

[matt_crouch]

ahh thanks a lot... one thing how do you mean that the motion is a "plane" pendulum?

 

[Dr.D]

The motion of the pendulum is always circular, no matter whether it is small amplitude or large amplitude. It does not depend on the length of the pendulum.

The reason for assuming small amplitudes is so that the equation of motion can be linearized and reduced to a harmonic differential equation. For this to apply, only small amplitudes can be considered.