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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.
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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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