# Modeling Simple Pendulum Essay

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Updated: May 4th, 2022

## Simple Pendulum

Gravity is responsible for an object falling toward Earth. The farther the object falls, the faster it is moving when it hits the ground. For each second that an object falls, its speed increases by a constant amount, called the acceleration due to gravity, denoted g. One way to calculate the value of g is to use a simple pendulum. Here is the accompanying figure.

T = 2π√l/g, where L equals the length of the pendulum. ### Solving the formula for g

To solve for g we have to make g the subject by doing the following

• T= 2∏√ (L/g) first we divide both sides by 2∏ we get
• T/2∏ = √ (L/g) then we square both sides
• (T/2∏)2 = L/g multiply by g on both sides
• g (T/2∏)2 = L dividing both sides by (T/2∏)2
• which gives as g=L/ (T/2∏)2

Rearranging the formula we have g = L (2∏/T) 2

### Determination of the value of g using the table to (The units for g are feet per second per second.)

By replacing the values in the formula, g = L (2∏/T) 2 we get the figures indicated in the table

 L(feet) T(seconds) (2∏/T)2 g (feet per second2) 0.5 0.78 64.9411638 32.47058 1.0 1.11 32.067368 32.06737 1.5 1.36 21.3614858 32.04223

### Interpretation of the result

Acceleration due to gravity is constant when it occurs within the earth’s atmosphere if the effect of air resistance was to be ignored. According to our results, we can see that g is ~ 32 ft/s2; this means that in absence of air, objects will fall by the same acceleration. The values for g, in this case, are not gravity but rather the acceleration due to gravity, which results when the force of gravity is the only force acting on an object. In conclusion, we realize that acceleration due to gravity is actually constant.

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