
A particle of mass m oscillates with simple harmonic motion between points \[{X_1}\] and \[{X_2}\], the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph:
A. 
B. 
C. 
D. 
Answer
162.3k+ views
Hint: If \[{X_1}\] and \[{X_2}\] represent two extreme positions then the potential energy(U) will be maximum at these points. At the point O which represents the equilibrium point then the potential energy(U) will be zero. If we plot a graph, it must show maximum values at \[{X_1}\] and \[{X_2}\] and also zero at O position.
Formula used:
Potential Energy in simple harmonic motion (SHM) is given as:
\[U = \dfrac{1}{2}k{x^2}\]
Where k is the force constant
x is a displacement
Complete step by step solution:
As we know that the for a particle of mass ‘m’ oscillates with simple harmonic motion (SHM) having Potential Energy,
\[U = \dfrac{1}{2}k{x^2}\]
This is in the form of parabolic equation which is in the form of \[y = {x^2}\]
At mean position, x=0 then the potential energy, U=0
Hence option A is the correct answer.
Note: Simple harmonic motion (SHM) is a type of an oscillatory motion in which the restoring force(F) is directly proportional to the displacement (x) of the particle from its mean position. The total energy of any particle while performing simple harmonic motion (SHM) is energy in simple harmonic motion. For the oscillatory motion, when a particle is at mean position it means at rest and when that particle reaches its extreme position then it comes to rest again. Thus, for the total energy in simple harmonic motion the kinetic energy and potential energy both must be calculated.
Formula used:
Potential Energy in simple harmonic motion (SHM) is given as:
\[U = \dfrac{1}{2}k{x^2}\]
Where k is the force constant
x is a displacement
Complete step by step solution:
As we know that the for a particle of mass ‘m’ oscillates with simple harmonic motion (SHM) having Potential Energy,
\[U = \dfrac{1}{2}k{x^2}\]
This is in the form of parabolic equation which is in the form of \[y = {x^2}\]
At mean position, x=0 then the potential energy, U=0
Hence option A is the correct answer.
Note: Simple harmonic motion (SHM) is a type of an oscillatory motion in which the restoring force(F) is directly proportional to the displacement (x) of the particle from its mean position. The total energy of any particle while performing simple harmonic motion (SHM) is energy in simple harmonic motion. For the oscillatory motion, when a particle is at mean position it means at rest and when that particle reaches its extreme position then it comes to rest again. Thus, for the total energy in simple harmonic motion the kinetic energy and potential energy both must be calculated.
Recently Updated Pages
A steel rail of length 5m and area of cross section class 11 physics JEE_Main

At which height is gravity zero class 11 physics JEE_Main

A nucleus of mass m + Delta m is at rest and decays class 11 physics JEE_MAIN

A wave is travelling along a string At an instant the class 11 physics JEE_Main

The length of a conductor is halved its conductivity class 11 physics JEE_Main

Two billiard balls of the same size and mass are in class 11 physics JEE_Main

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

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

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

Class 11 JEE Main Physics Mock Test 2025

JoSAA JEE Main & Advanced 2025 Counselling: Registration Dates, Documents, Fees, Seat Allotment & Cut‑offs

Other Pages
NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

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

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

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

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

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