The use of a simple pendulum experiment in the study of motion helps to provide valuable insights into the acceleration of objects due to the gravitation force. In this experiment, a mass is suspended from one end of a piece of string and set in motion to determine the number of oscillations in a particular period. Such an oscillatory motion (to and from motion) is referred to as simple harmonic motion. The time a pendulum takes to swing forth and back is affected by factors such as the pendulum’s length and the acceleration due to the gravitation. A shorter pendulum has a shorter period to complete a single oscillation than a longer pendulum. In view of this, this simple pendulum experiment used the relation between the length applied in the pendulum and the time of oscillation to estimate the value of acceleration due to the gravitation force (Avison & Caribbean Examinations Council, 1988).
The simple pendulum experiment was mainly conducted to facilitate the understanding of the relationship between different parameters in an oscillatory system. In addition, the experiment seeks to use its data analysis to facilitate the calculation of a value for the gravitational acceleration (g) and compare this value with the widely accepted value of 9.81 m/s2.
If a mass of m hangs from the string in a simple pendulum experiment and sets to swing with small amplitude, the mass will oscillate back and forth in a simple harmonic motion. In this scenario, the mass of the bob becomes the inertia as the tangential component changes the direction every time the bob (mass) passes the center of its swing and hence acting to restore the mass to its midpoint. For this reason, the restoring force, F = - mg sin (ᴓ).
However, if the angle ᴓ is very small, then it is assumed that sin (ᴓ) ≈ ᴓ, hence, F = - magᴓ….. Equation (1). The angle ᴓ of displacementᴓ can be determined from the equilibrium using the arc length, x,