How Do You Calculate the Frequency of a Pendulum?

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To calculate the frequency of a pendulum, the formula f = 1/T is used, where T represents the period of one complete cycle. In this case, the pendulum takes 0.5 seconds to swing from its highest point to the equilibrium position, which is half of the full cycle. Therefore, the total period T is 1 second. Substituting this value into the frequency formula gives f = 1/1, resulting in a frequency of 1 Hz. The discussion clarifies that the frequency of the pendulum is 1 Hz based on the calculated period.
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Vibrations Assignment Please Help!

Homework Statement


A pendulum takes 0.5s to swing from its hgihest point to the equilibrium position. What is the frequency of the pendulum?


Homework Equations


f = 1/T


The Attempt at a Solution


So would it be this?
f = 1/T
f = 1/0.5
f = 2Hz
 
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f=1/T T is the period. The period is how long it takes to make one complete cycle. How long will it take for the pendulum bob to swing from its highest point, through the complete range of motion eventually ending back to the original starting position? That time is T.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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