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The P.E. function of a particle executing linear simple harmonic motion is given by V (x) = 1/2 kx2, where k, force constant of oscillator is equal to 0.5 N/m. The amplitude of particle when its total energy is 1 J is equal to
  • a)
    2 √2 m
  • b)
    2 m
  • c)
    √2 m
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?
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To find the amplitude of the particle, we need to find the value of x when the total energy is 1 J.

The total energy of the particle is the sum of its kinetic energy (KE) and potential energy (PE). In simple harmonic motion, the kinetic energy is given by KE = 1/2 mv^2, where m is the mass of the particle and v is its velocity.

The potential energy is given by PE = 1/2 kx^2, where k is the force constant and x is the displacement from the equilibrium position.

Since the total energy is given as 1 J, we have:

1 J = KE + PE
1 J = 1/2 mv^2 + 1/2 kx^2

We can rearrange this equation to solve for x:

1 J - 1/2 mv^2 = 1/2 kx^2
1/2 kx^2 = 1 J - 1/2 mv^2
kx^2 = 2 J - mv^2
x^2 = (2 J - mv^2)/k
x = sqrt((2 J - mv^2)/k)

Since we are given that the force constant k = 0.5 N/m, we can substitute this value into the equation:

x = sqrt((2 J - mv^2)/(0.5 N/m))

However, we do not have enough information to determine the values of m and v. Therefore, we cannot calculate the amplitude of the particle when its total energy is 1 J.
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The P.E. function of a particle executing linear simple harmonic motion is given by V (x) = 1/2 kx2, where k, force constant of oscillator is equal to 0.5 N/m. The amplitude of particle when its total energy is 1 J is equal toa)2 √2 mb)2 mc)√2 md)None of theseCorrect answer is option 'B'. Can you explain this answer?
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