JEE Exam > JEE Questions > A particle perform S.H.M of amplitude A along...
Start Learning for Free
A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes,
?
Most Upvoted Answer
A particle perform S.H.M of amplitude A along a straight line . when i...
Explanation:
To solve the given problem, we need to understand the concept of Simple Harmonic Motion (S.H.M) and impulsive forces.
Simple Harmonic Motion (S.H.M):
S.H.M is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts towards the equilibrium position. The equation of S.H.M is given by:
x = A * sin(ωt + φ)
where,
x = displacement from the mean position
A = amplitude of the motion
ω = angular frequency
t = time
φ = phase constant
Impulsive Force:
An impulsive force is a force that acts on a body for a very short duration of time. It changes the momentum of the body instantaneously and causes a sudden change in its velocity.
Given:
Amplitude of S.H.M (A) = A
Distance from mean position (x) = 3/2A
Increase in K.E (ΔKE) = U * T.M.E
Solution:
1. Let's assume the initial position of the particle is at the mean position (x = 0).
2. At a distance of 3/2A from the mean position, the particle will have a displacement of x = 3/2A.
3. Using the equation of S.H.M, we can find the value of ωt + φ at x = 3/2A.
3/2A = A * sin(ωt + φ)
sin(ωt + φ) = 3/2
ωt + φ = sin^(-1)(3/2)
ωt + φ = π/2
ωt = π/2 - φ
4. Now, let's consider the impulsive force acting on the particle. Due to this force, the particle's K.E increases by an amount ΔKE = U * T.M.E.
ΔKE = U * T.M.E = U * (1/2) * (mω^2A^2)
5. The new amplitude of the particle's motion can be calculated using the relation between K.E and amplitude.
ΔKE = (1/2) * mω^2 * (A^2 - A'^2)
U * (1/2) * (mω^2A^2) = (1/2) * mω^2 * (A^2 - A'^2)
U * A^2 = A^2 - A'^2
A'^2 = A^2 - U * A^2
A' = A * √(1 - U)
Therefore, the new amplitude of the particle's motion is A * √(1 - U).
To solve the given problem, we need to understand the concept of Simple Harmonic Motion (S.H.M) and impulsive forces.
Simple Harmonic Motion (S.H.M):
S.H.M is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts towards the equilibrium position. The equation of S.H.M is given by:
x = A * sin(ωt + φ)
where,
x = displacement from the mean position
A = amplitude of the motion
ω = angular frequency
t = time
φ = phase constant
Impulsive Force:
An impulsive force is a force that acts on a body for a very short duration of time. It changes the momentum of the body instantaneously and causes a sudden change in its velocity.
Given:
Amplitude of S.H.M (A) = A
Distance from mean position (x) = 3/2A
Increase in K.E (ΔKE) = U * T.M.E
Solution:
1. Let's assume the initial position of the particle is at the mean position (x = 0).
2. At a distance of 3/2A from the mean position, the particle will have a displacement of x = 3/2A.
3. Using the equation of S.H.M, we can find the value of ωt + φ at x = 3/2A.
3/2A = A * sin(ωt + φ)
sin(ωt + φ) = 3/2
ωt + φ = sin^(-1)(3/2)
ωt + φ = π/2
ωt = π/2 - φ
4. Now, let's consider the impulsive force acting on the particle. Due to this force, the particle's K.E increases by an amount ΔKE = U * T.M.E.
ΔKE = U * T.M.E = U * (1/2) * (mω^2A^2)
5. The new amplitude of the particle's motion can be calculated using the relation between K.E and amplitude.
ΔKE = (1/2) * mω^2 * (A^2 - A'^2)
U * (1/2) * (mω^2A^2) = (1/2) * mω^2 * (A^2 - A'^2)
U * A^2 = A^2 - A'^2
A'^2 = A^2 - U * A^2
A' = A * √(1 - U)
Therefore, the new amplitude of the particle's motion is A * √(1 - U).
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced?
Question Description
A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced?.
A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced?.
Solutions for A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced? defined & explained in the simplest way possible. Besides giving the explanation of
A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced?, a detailed solution for A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced? has been provided alongside types of A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced? theory, EduRev gives you an
ample number of questions to practice A particle perform S.H.M of amplitude A along a straight line . when it is at a distance 3/2A from mean position , it's K.E gets increased by an amount U,(x)( T.M.E) due to an impulsive force Then it's New amplitude becomes, Related: Syllabus covered in each Part Test of JEE Advanced? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup