The gravitational potential energy of an object refers to the energy an object possesses due to its location relative to a reference point. Considering an object close the Earth’s surface the gravitational potential energy is given as (Cutnell et al. 18)
Where g is the gravitational acceleration, m is the mass if the object and y are the vertical position of the object relative to an arbitrary reference point. The following graphical plot illustrates the variation of kinetic and potential energy of the oscillating systems studied in this lab
For a swinging pendulum (oscillatory system) there is the constant conversion of energy to kinetic energy, potential energy and back to kinetic energy however the total energy at any given time is always a constant. The energy stored in compressed springs or elastic objects is another form of potential energy that is mathematically given as (Cutnell et al. 25).
Notably, when there is no energy input into the system, the total mechanical energy will remain constant. The linear plot shown in the printout shows the constancy of mechanical energy with time defined by same slope over given time. Using the K/m and y values shown in the table of results above the following graphical plot was obtained that shows the relationship between the K/m and the vertical displacement
Using the Excel graphical plot above the gravitational acceleration was evaluate because for an oscillating system like a pendulum maximum potential energy (maximum displacement) is experienced when the kinetic energy is at a minimum. Equally maximum kinetic energy for a simple pendulum corresponds to the point where there is minimum vertical displacement.
At the point where K/m is equal to zero, the potential energy of the system is at a maximum this corresponds to the point where the value of the arbitrary displacement is 0.1089. The potential energy per unit mass at this point