Rearranging period of pendulum equation to find length

In summary, to find the length of a pendulum using the period equation, use the formula T = 2π√(L/g) and solve for L by dividing both sides by (2π)^2 and squaring. The units for the period are seconds (s), and any consistent units can be used for length and acceleration. This equation can be used for any pendulum in simple harmonic motion as long as the acceleration due to gravity is known.
  • #1
Adam17
16
0

Homework Statement

What is
T=2pi[(sqrt)l/g] rearranged for l= ?



Homework Equations





The Attempt at a Solution


Ive tried a few but I just don't know how to do this with sqrt's of a fraction involved.
 
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  • #2
Eliminate the square root by squaring both sides.
 
  • #3
Ok,so what I end up with after that is l=T^2g/2pi. Which is wrong as its not giving me the correct answer.
 
  • #4
When you square both sides, don't forget that you also have to square the factor of 2[itex]\pi[/itex]
 
  • #5



To rearrange the period of a pendulum equation to solve for the length, we can follow these steps:

1. Start with the original equation: T=2pi[(sqrt)l/g]

2. Square both sides of the equation to eliminate the square root: T^2 = 4pi^2(l/g)

3. Multiply both sides by g to isolate the length variable: gT^2 = 4pi^2l

4. Divide both sides by 4pi^2 to solve for l: l = gT^2 / 4pi^2

Therefore, the equation for length (l) in terms of period (T) and acceleration due to gravity (g) is l = gT^2 / 4pi^2. This equation can be used to calculate the length of a pendulum based on its period and the acceleration due to gravity in a specific location.
 

FAQ: Rearranging period of pendulum equation to find length

1. How do I rearrange the period of pendulum equation to find the length?

To rearrange the period of pendulum equation to find the length, you can use the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. You can rearrange this equation to solve for L by dividing both sides by (2π)^2 and then squaring both sides.

2. What is the formula for the period of a pendulum?

The formula for the period of a pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

3. Can I use any units for the length and acceleration in the pendulum equation?

Yes, you can use any units for the length and acceleration in the pendulum equation as long as they are consistent. For example, if you use meters for length, then you should use meters per second squared for acceleration.

4. What are the units for the period in the pendulum equation?

The units for the period in the pendulum equation are seconds (s).

5. Can I use the pendulum equation to find the length of any pendulum?

Yes, the pendulum equation can be used to find the length of any pendulum as long as the pendulum is in simple harmonic motion and the acceleration due to gravity is known. However, for more complex pendulum systems, different equations may need to be used.

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