Added the algorithm to compute the time period of a simple pendulum (#…

…10265)

* Added the algorithm to compute the time period of a simple pendulum

* imported g form scipy and changed doctests accordingly

* fixed formatting

* applied all suggested changes from code review

* Apply suggestions from code review

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---------

Co-authored-by: Tianyi Zheng <[email protected]>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

physics/period_of_pendulum.py

@@ -0,0 +1,53 @@
+"""
+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
+
+from scipy.constants import g
+
+
+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
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()