
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
164.4k+ views
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.
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.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
