How to Calculate g with Known Pendulum Length and Negligible Amplitude?

[Bibigul]

How to calculate g if amplitude of a simple pendulum is negligible and the length is known?




T=2π$\sqrt{}l/g$

 

[Doc Al]

In terms of the period? Just solve for g in terms of T and L.

 

[Bibigul]

No, only in terms of L.

 

[Simon Bridge]

Check your problem:
Why should the length L depend on the strength of gravity? This is usually something you just cut to whatever length you like - 1m on Jupiter is the same as 1m on the moon... unless, I suppose, you are doing the measuring from a different gravity from the one the meter is in? (This forum I don't want to make too many assumptions!)

 

[asteriatic]

To calculate the value of g, we can rearrange the above equation to solve for g:
g=4π^2l/T^2

In this case, since the amplitude of the simple pendulum is negligible, we can assume that the time period (T) is the time it takes for the pendulum to complete one full swing. Therefore, we can measure the time it takes for the pendulum to complete a certain number of swings and use that value for T in the equation above.

It is important to note that this calculation will only provide an estimate of the value of g, as there may be other factors such as air resistance that can affect the motion of the pendulum. To get a more accurate measurement of g, multiple trials should be conducted and the average value should be taken. Additionally, the length of the pendulum should be measured accurately to ensure the reliability of the calculation.