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Why does mass not matter in a Pendulum Period?
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What is the physics behind mass not affecting the period?
The reason that mass is irrelevant is because although it requires more energy to move the larger mass, the restoring force of the pendulum is apparent on the tangential axis which uses mgsinθ. What this does is
is allow for gravity to account for the extra force that is needed due to the larger
mass
Example
Mathematical Reasoning
There are two simple pendulums side by side, both with a string length of 0.3m, but one has a mass of 4kg and the other a mass of 2kg. Which of the following statements is correct?
a) The 4kg pendulum has a faster period
b) The 2kg pendulum has a faster period
c) Their periods will be the same
d) Not enough information to tell
Period is given by :
This shows that mass is not a factor in determining the period so if all the other variables are the same, the periods of each will match.
Answer
C) is the correct answer. This is because there will be no difference in the oscillations because mass does not matter in a simple pendulum. With a simple pendulum gravity is the key force in driving the pendulum which is proportional to the mass.
Oscillation of a Pendulum
When it comes to the simple pendulum, the vital part of understanding what is actually occurring in order to have an idea of what the outcome should be. An example of this if you have problem where two pendulums are present with the same length, but different masses, will they have the same oscillation or not?