JEE Exam > JEE Questions > A particle of mass m is executing oscillation...
Start Learning for Free
A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION.
Most Upvoted Answer
A particle of mass m is executing oscillations about the origin on x a...
Introduction:
In this problem, we need to find the time period of oscillation of a particle with a potential energy function of U(x) = k|x|^3.
Solution:
To find the time period, we can use the formula:
T = 2π√(m/k)
where m is the mass of the particle and k is the spring constant.
Finding the spring constant:
Since the potential energy of the particle is U(x) = k|x|^3, we can find the force on the particle by taking the derivative of the potential energy function:
F(x) = -dU(x)/dx
F(x) = -3kx|x|
This force is a restoring force, which means that it always acts towards the equilibrium position (x=0). Therefore, we can write:
F(x) = -kx
where k = 3ka^2
Finding the time period:
Substituting the value of k in the formula for time period, we get:
T = 2π√(m/3ka^2)
Simplifying this expression, we get:
T = 2π√(m/3k) * 1/a
Therefore, the time period is proportional to 1/root(a).
Conclusion:
The time period of oscillation of a particle with a potential energy function of U(x) = k|x|^3 is proportional to 1/root(a). This means that as the amplitude of oscillation increases, the time period decreases.
In this problem, we need to find the time period of oscillation of a particle with a potential energy function of U(x) = k|x|^3.
Solution:
To find the time period, we can use the formula:
T = 2π√(m/k)
where m is the mass of the particle and k is the spring constant.
Finding the spring constant:
Since the potential energy of the particle is U(x) = k|x|^3, we can find the force on the particle by taking the derivative of the potential energy function:
F(x) = -dU(x)/dx
F(x) = -3kx|x|
This force is a restoring force, which means that it always acts towards the equilibrium position (x=0). Therefore, we can write:
F(x) = -kx
where k = 3ka^2
Finding the time period:
Substituting the value of k in the formula for time period, we get:
T = 2π√(m/3ka^2)
Simplifying this expression, we get:
T = 2π√(m/3k) * 1/a
Therefore, the time period is proportional to 1/root(a).
Conclusion:
The time period of oscillation of a particle with a potential energy function of U(x) = k|x|^3 is proportional to 1/root(a). This means that as the amplitude of oscillation increases, the time period decreases.
Community Answer
A particle of mass m is executing oscillations about the origin on x a...
P.E.=kx³..... F=-du/Dx=-3kx²....max force=-3ka²=-mw²a....w²=3ka/m.....nd w²also equals to 4π²/T².... comparing both T directly proportional to 1/√a..
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
|
|
Similar JEE Doubts
Top Courses for JEEView all
A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION.
Question Description
A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION. 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 of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION. covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION..
A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION. 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 of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION. covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION..
Solutions for A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION. 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 of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION. defined & explained in the simplest way possible. Besides giving the explanation of
A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION., a detailed solution for A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION. has been provided alongside types of A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION. theory, EduRev gives you an
ample number of questions to practice A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? *proportional to 1/root a *independent of a *proportional to root a *proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION. 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!
within 7 days!
Takes less than 10 seconds to signup