Question

A body executing SHM has its velocity \[16\,cm/s\] when passing through the mean position. If it goes $1\,cm$ either side of the mean position, then find its maximum period.

Answer 1

Hint: In the case of a problem based on SHM (Simple Harmonic Motion), we know that all the parameters vary with each other such as frequency, amplitude, mean position, phase difference, etc., hence, analyze every aspect of the solution with the scientific approach and check which one seems to be more appropriate for the given situation. Then, present the answer with a proper explanation.

Formula usd:
The formula of maximum time period is,
$T = \dfrac{\text{displacement(d)}}{\text{velocity(v)}}$
Here, $T$ is the time period.

Complete step by step solution:
Velocity of a body executing SHM $v = 16cm/s = 16 \times {10^{ - 2}}m/s$ (given)
A body goes $d = 1cm = {10^{ - 2}}m$ either side of the mean position. (given)

We know that Simple Harmonic Motion or SHM is an oscillatory motion where the restoring force is directly proportional to the displacement of the body from its mean position. According to the question, displacement from mean position and velocity is given. We can easily apply the basic fundamentals of physics to calculate the time taken by the body for the given displacement.

Also, we know that in case of SHM, maximum time period can be calculated as:
Maximum time period,
$T = \dfrac{\text{displacement(d)}}{\text{velocity(v)}}$
$ \Rightarrow T = \dfrac{{{{10}^{ - 2}}}}{{16 \times {{10}^{ - 2}}}}$
$ \therefore T = 0.0625\,s$

Hence, the maximum time period for a body executing SHM is $0.0625$ seconds.

Note: Since this is a problem based on SHM (Simple Harmonic Motion) hence, it is essential that given conditions be analyzed very carefully to give an accurate solution. While writing answers to this kind of conceptual problem, always keep in mind to identify the parameters provided in a problem.