The potential energy (PE) of a simple harmonic oscillator is given by the formula PE = 1/2 kx^2, where k is the spring constant and x is the displacement from the equilibrium position.

When the particle is at its endpoint, the potential energy is at its maximum and equals the total energy E.

When the particle is halfway to its endpoint, the displacement x is halved. Therefore, the potential energy is 1/2 k (x/2)^2 = 1/2 kx^2 / 4 = E / 4.

So, the potential energy of the simple harmonic oscillator when the particle is halfway to its endpoint is E/4 of the total energy E.

None of the options (a) 18E, (b) 14E, (c) 12E, (d) 23E match this result. There might be a mistake in the question or the provided options.

Question

The potential energy (PE) of a simple harmonic oscillator is given by the formula PE = 1/2 kx^2, where k is the spring constant and x is the displacement from the equilibrium position.

When the particle is at its endpoint, the potential energy is at its maximum and equals the total energy E.

When the particle is halfway to its endpoint, the displacement x is halved. Therefore, the potential energy is 1/2 k (x/2)^2 = 1/2 kx^2 / 4 = E / 4.

So, the potential energy of the simple harmonic oscillator when the particle is halfway to its endpoint is E/4 of the total energy E.

None of the options (a) 18E, (b) 14E, (c) 12E, (d) 23E match this result. There might be a mistake in the question or the provided options.

Knowee AI · Accepted Answer

The potential energy (PE) of a simple harmonic oscillator is given by the formula PE = 1/2 kx^2, where k is the spring constant and x is the displacement from the equilibrium position.

When the particle is at its endpoint, the potential energy is at its maximum and equals the total energy E.

When the particle is halfway to its endpoint, the displacement x is halved. Therefore, the potential energy is 1/2 k (x/2)^2 = 1/2 kx^2 / 4 = E / 4.

So, the potential energy of the simple harmonic oscillator when the particle is halfway to its endpoint is E/4 of the total energy E.

None of the options (a) 18E, (b) 14E, (c) 12E, (d) 23E match this result. There might be a mistake in the question or the provided options.

The potential energy of a simpleharmonic oscillator when the particle ishalf way to its end point is (where E isthe total energy).(a) 18 𝐸(b) 14 𝐸(c) 12 𝐸(d) 23 𝐸

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