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""" | ||
Title : Computing the time period of a simple pendulum | ||
The simple pendulum is a mechanical system that sways or moves in an | ||
oscillatory motion. The simple pendulum comprises of a small bob of | ||
mass m suspended by a thin string of length L and secured to a platform | ||
at its upper end. Its motion occurs in a vertical plane and is mainly | ||
driven by gravitational force. The period of the pendulum depends on the | ||
length of the string and the amplitude (the maximum angle) of oscillation. | ||
However, the effect of the amplitude can be ignored if the amplitude is | ||
small. It should be noted that the period does not depend on the mass of | ||
the bob. | ||
For small amplitudes, the period of a simple pendulum is given by the | ||
following approximation: | ||
T ≈ 2π * √(L / g) | ||
where: | ||
L = length of string from which the bob is hanging (in m) | ||
g = acceleration due to gravity (approx 9.8 m/s²) | ||
Reference : https://byjus.com/jee/simple-pendulum/ | ||
""" | ||
from math import pi | ||
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from scipy.constants import g | ||
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def period_of_pendulum(length: float) -> float: | ||
""" | ||
>>> period_of_pendulum(1.23) | ||
2.2252155506257845 | ||
>>> period_of_pendulum(2.37) | ||
3.0888278441908574 | ||
>>> period_of_pendulum(5.63) | ||
4.76073193364765 | ||
>>> period_of_pendulum(-12) | ||
Traceback (most recent call last): | ||
... | ||
ValueError: The length should be non-negative | ||
>>> period_of_pendulum(0) | ||
0.0 | ||
""" | ||
if length < 0: | ||
raise ValueError("The length should be non-negative") | ||
return (2 * pi) * (length / g) ** 0.5 | ||
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if __name__ == "__main__": | ||
import doctest | ||
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doctest.testmod() |
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