Derive the expression for the time period of a simple pendulum if the period of oscillations depends on its length and accelaration due to gravity.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember the formula of constant of simple pendulum such that:

k = L/T^2

You need to consider the value of constant equivalent to g/(4pi^2) (g expresses the gravity acceleration)

You need to set the equations g/(4pi^2) and L/T^2 equal such that:

L/T^2 = g/(4pi^2)

You need to find time period such that:

g*T^2 = 4pi^2*L

T^2 = (4pi^2*L)/g => T = 2pi*sqrt(L/g)

Hence, evaluating the time period of simple pendulum under given conditions yields T = 2pi*sqrt(L/g).

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