Question

To understand the relationships of the energetics, forces, acceleration, and velocity of an oscillating pendulum, and to determine how the motion of a pendulum depends on the mass, the length of the string, and the acceleration due to gravity.

For this tutorial, use the PhET simulation Pendulum Lab. This simulation mimics a real pendulum and allows you to adjust the initial position, the mass, and the length of the pendulum.
You can drag the pendulum to an arbitrary initial angle and release it from rest. You can adjust the length and the mass of the pendulum using the slider bars at the top of the green panel. Velocity and acceleration vectors can be selected to be shown, as well as the forms of energy.


J. Now, change the planet where the experiment takes place to see how the period of oscillation depends on the acceleration due to gravity, g (on Earth, g =10 m/s/s; g is larger than this value on Jupiter and smaller than this value on the Moon). How does the period of oscillation depend on the value of g?

Answer 1

The period of a simple pendulum is inversely proportional to the square root of the acceleration due to gravity; it decreases with higher gravity and increases with lower gravity, independent of mass or small swing amplitudes.

Step-by-step explanation:

The period of oscillation of a simple pendulum is determined by its length and the acceleration due to gravity (g). According to the mathematical formula for the period (T) of a simple pendulum, T = 2π√(l/g), where 'l' is the pendulum length and 'g' is the acceleration due to gravity. This shows that the period of a pendulum is inversely proportional to the square root of the acceleration due to gravity. Therefore, if the acceleration due to gravity increases (as it would on a planet like Jupiter), the period decreases; conversely, if g decreases (as on the Moon), the period increases. Importantly, the mass of the pendulum and the amplitude of the swing do not affect the period, as long as the amplitude is relatively small (< 15°).