How will the oscillation period of the pendulum change if the mass of the ball is doubled and

How will the oscillation period of the pendulum change if the mass of the ball is doubled and the length of the pendulum thread is reduced by 4 times?

The oscillation period of the pendulum is given by the formula:
T = 2 * pi * root (l / g) (1),
where l is the length of the thread, g is the acceleration of gravity.
There is no mass in the formula, therefore, the period does not depend on the mass.
Let’s write the formula for the changed length:
T₁ = 2 * pi * root (l / 4g) = pi * root (l / g) (2).
Comparing (1) and (2), we see that with a decrease in the length of the thread by 4 times, the period decreased by half.

Answer: The oscillation period will be halved.



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