Question

The mean time period of a simple pendulum is $1.92s$. Mean absolute erroring the time period is $0.05s$. To express the maximum estimate of error, the time period should be written as:
A. $T=(1.92\pm 0.01)s$
B. $T=(1.92\pm 0.25)s$
C. $T=(1.92\pm 0.05)s$
D. $T=(1.92\pm 0.10)s$

Answer 1

Hint: The time period of a simple pendulum is the time taken by the pendulum to finish a full oscillation (cycle). It is denoted by $T$. The absolute error is the difference between the measured and the actual value of the time period of the simple pendulum. The maximum estimated error can be found using these two quantities.

Complete step by step answer:
As per the given data,
Mean time period of the pendulum $1.92s$
Absolute error is $0.05s$
When taking readings of the time period the measured value can differ from the actual theoretical value of the time period. This difference between these values is known as the absolute error. This error can be either positive or negative. So while calculating the maximum error both the situations are taken into consideration.
So, the maximum estimated error of the simple pendulum will be the submission of the mean time period and the mean absolution of the simple pendulum.
Mathematically,
$T=(1.92\pm 0.05)s$
This value $T$ is the required answer.

So, the correct answer is “Option C”.

Note: A simple pendulum is one that can be considered to be a point mass attached to a string or rod of least (negligible) mass. It is a system with frequency resonant frequency. When there are no losses the simple pendulum shows a wave of a sinusoidal wave. In presence of friction (air friction) or retarding force the simple pendulum undergoes damped oscillation. In damped oscillation, the amplitude of the wave decreases regularly and after a certain period of time, the pendulum comes to rest.