If T is the time period of an oscillating pendulum, which one of the f

If T is the time period of an oscillating pendulum, which one of the following statements is NOT correct ?

[amp_mcq option1=”The motion repeats after time T only once” option2=”T is the least time after which motion repeats itself” option3=”The motion repeats itself after nT, where n is a positive integer” option4=”T remains the same only for small angular displacements” correct=”option1″]

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UPSC NDA-1 – 2018

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The time period (T) of an oscillating pendulum is defined as the smallest time interval after which the motion repeats itself. While the motion does repeat after time T, it also repeats after any integer multiple of T (2T, 3T, 4T, etc.). Therefore, the statement that the motion repeats after time T “only once” is incorrect. The oscillation continues to repeat after every interval of T.

– A periodic motion repeats itself after a fixed interval of time called the time period.
– The time period T is the *minimum* time for the motion to repeat.
– The motion repeats after nT, where n is a positive integer.

For a simple pendulum undergoing Simple Harmonic Motion (SHM) at small angles, the time period is given by T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. For larger angles, the period is slightly longer and depends on the amplitude, making the statement D (T remains the same only for small angular displacements) correct for the conditions under which the simple pendulum formula is typically derived.

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