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Physics Curiosity

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- Homework Statement
- Question requires you to 'process' the independent variable, (the thing that's manipulated thing on a pendulum),

- Relevant Equations
- The simple pendulum equation is T = 2π√(L/g), in which the independent variable "L" is 'processed' into T = 2π/√(g) * √(L). I am wondering how in this equation, T = 2π√(2L/3g), how the 2L can be processed into √(L) like the first example of the simple pendulum equation being processed?

Initially I went from:

T = 2π√(2L/3g)

T = 2π/√(3g) * √(2L)

To finally this equation:

T = 2π/√(3g) * √(L)

Where 2L becomes L as the 2 is lost. I am not fully sure if this is correct or how to properly get rid of the 2 in 2L.We must follow the rule of y = mx+c whereby y = T, m = the constant variables (pi and g), and x is the independent variable (L). There is no y-intercept c. Hence the equation must be 'processed' in this way.

T = 2π√(2L/3g)

T = 2π/√(3g) * √(2L)

To finally this equation:

T = 2π/√(3g) * √(L)

Where 2L becomes L as the 2 is lost. I am not fully sure if this is correct or how to properly get rid of the 2 in 2L.We must follow the rule of y = mx+c whereby y = T, m = the constant variables (pi and g), and x is the independent variable (L). There is no y-intercept c. Hence the equation must be 'processed' in this way.

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