An object that is released freely, for example, moves towards the center of the earth with an increasing velocity. Similarly, an object thrown upwards moves with a decreasing rate before it comes to rest and then accelerates downwards. Newton hypothesized the existence of a force, the force of gravity that attracts objects towards its center, explaining the observation. The muscle acts in the same direction as the direction of motion of an object towards the center of the earth and thus increases velocity. However, it counters movements away from the center of the planet and therefore reduces the rate of the associated object (Agarwal 2011, p. 442. McGinnis2013, p. 22). In the absence of any other external force that could act on an item, the realized power is called acceleration due to gravity and is a constant for all objects within the earth’s surface and a limit of the earth’s environment (Chabay and Sherwood 2011, p. 6).

When a mass on a simple pendulum is displaced, it moves in a vertical plane, and for small displacements, the motion of the object assumes a harmonic motion. Newton’s second law of motion then explains the object’s move from an angular perspective, as shown below.

F=ma

This translates to the equation,

F=-again&nbsp.θ &nbsp.

For small values of θ, however, sin&nbsp.θ=&nbsp.θ and this changes the equation to F=-mg θ

Expressing force as a second-order derivative of angular displacement and eliminating m from both sides generates the following as the resulting equation of motion.

D2 θ/dt2 =-(g/L) θ

With the angular frequency = (g/L) 0.5, the following is the equation for the period.

(Serway and Jewett 2009, p. 448)

From the equation, a direct proportionality relation is identifiable between the period for an oscillation and the length of a pendulum, as shown below.

T=2πg-0.5l0.5

This can also be expressed as T2=4π2l/g

And

T2=(4π2/g) l

This allows for the graphical determination of acceleration’s value due to gravity from the gradient of the graph of the period versus length of the string used in an experiment. From the graph,

Gradient= 4π2/g

g=4π2/ gradient

Similarly, the value of g can be calculated empirically from the equation and for a single trial. The formula for determining g is as follows.