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A particle of mass 1 kg is executing SHM and its potential energy is given is is u =( x^2 - 4 x 3) joule then find its amplitude if velocity at mean position is 2√6 metre per second?
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A particle of mass 1 kg is executing SHM and its potential energy is g...
Given Information:
- Mass of the particle (m) = 1 kg
- Potential energy (u) = x^2 - 4x + 3 J
Formula:
The potential energy (u) of a particle executing Simple Harmonic Motion (SHM) is given by:
u = ½ kx^2
where k is the force constant and x is the displacement from the mean position.
Step 1: Find the Force Constant (k):
Comparing the given potential energy equation with the formula for potential energy, we can find the force constant.
Comparing the coefficients, we get:
k = 1
Step 2: Find the Amplitude (A):
The amplitude (A) of an SHM can be determined using the velocity at the mean position.
The velocity at the mean position is given as 2√6 m/s.
Formula:
The velocity of a particle in SHM is given by:
v = ωA
where v is the velocity, ω is the angular frequency, and A is the amplitude.
Step 3: Find the Angular Frequency (ω):
To find the angular frequency, we can use the relation between force constant and angular frequency in SHM.
The formula is given by:
ω = √(k/m)
where ω is the angular frequency, k is the force constant, and m is the mass of the particle.
Substituting the known values, we get:
ω = √(1/1) = 1 rad/s
Step 4: Find the Amplitude (A):
Using the velocity at the mean position and the angular frequency, we can find the amplitude.
The formula is given by:
A = v/ω
Substituting the known values, we get:
A = (2√6)/(1) = 2√6 m
Therefore, the amplitude of the particle executing SHM is 2√6 meters.
- Mass of the particle (m) = 1 kg
- Potential energy (u) = x^2 - 4x + 3 J
Formula:
The potential energy (u) of a particle executing Simple Harmonic Motion (SHM) is given by:
u = ½ kx^2
where k is the force constant and x is the displacement from the mean position.
Step 1: Find the Force Constant (k):
Comparing the given potential energy equation with the formula for potential energy, we can find the force constant.
Comparing the coefficients, we get:
k = 1
Step 2: Find the Amplitude (A):
The amplitude (A) of an SHM can be determined using the velocity at the mean position.
The velocity at the mean position is given as 2√6 m/s.
Formula:
The velocity of a particle in SHM is given by:
v = ωA
where v is the velocity, ω is the angular frequency, and A is the amplitude.
Step 3: Find the Angular Frequency (ω):
To find the angular frequency, we can use the relation between force constant and angular frequency in SHM.
The formula is given by:
ω = √(k/m)
where ω is the angular frequency, k is the force constant, and m is the mass of the particle.
Substituting the known values, we get:
ω = √(1/1) = 1 rad/s
Step 4: Find the Amplitude (A):
Using the velocity at the mean position and the angular frequency, we can find the amplitude.
The formula is given by:
A = v/ω
Substituting the known values, we get:
A = (2√6)/(1) = 2√6 m
Therefore, the amplitude of the particle executing SHM is 2√6 meters.
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A particle of mass 1 kg is executing SHM and its potential energy is given is is u =( x^2 - 4 x 3) joule then find its amplitude if velocity at mean position is 2√6 metre per second?
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A particle of mass 1 kg is executing SHM and its potential energy is given is is u =( x^2 - 4 x 3) joule then find its amplitude if velocity at mean position is 2√6 metre per second? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle of mass 1 kg is executing SHM and its potential energy is given is is u =( x^2 - 4 x 3) joule then find its amplitude if velocity at mean position is 2√6 metre per second? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 1 kg is executing SHM and its potential energy is given is is u =( x^2 - 4 x 3) joule then find its amplitude if velocity at mean position is 2√6 metre per second?.
A particle of mass 1 kg is executing SHM and its potential energy is given is is u =( x^2 - 4 x 3) joule then find its amplitude if velocity at mean position is 2√6 metre per second? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle of mass 1 kg is executing SHM and its potential energy is given is is u =( x^2 - 4 x 3) joule then find its amplitude if velocity at mean position is 2√6 metre per second? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 1 kg is executing SHM and its potential energy is given is is u =( x^2 - 4 x 3) joule then find its amplitude if velocity at mean position is 2√6 metre per second?.
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