What is the arc length of a pendulum bob with mass m and length l?

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The arc length of a pendulum bob can be expressed as the product of the angle of displacement (theta) and the length of the string (l). However, the challenge arises because the angle of displacement is not always known. To determine the arc length accurately, one must consider the maximum angle of displacement. This relationship highlights the dependency of arc length on the angle, which is a crucial aspect of pendulum motion. Understanding this concept is essential for analyzing pendulum dynamics effectively.
william kat
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a pendulum bob of mass m hangs on a string of length l. what is the espression for the arc length of the bob if its discplaced through an angle theta.
 
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well if you know the maximum angle of displacement the arc length is simply

theta*l
 
problem is, the angle of discplacement is not known. its part of the expression
 

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