Question

Figure 10.20 in your textbook shows an energy diagram for a system with total energy E1. Suppose the system's total energy is E2 = (1/3)E1. In what ways could the particle move?
Select all that apply.

a.) It could remain at rest at x3.
b.) It could oscillate between x1 and x5.
c.) It could undergo small oscillations around x2.
d.) It could undergo small oscillations around x3.
e.) It could undergo small oscillations around x4.

Please explain why, I have an exam coming up and want to understand the concept.

Answer 1

The particles can undergo small oscillations around x₂.

The given parameters;

• initial energy of the particles = E₁
• final energy of the particles, E₂ = 0.33E₁

The movement of the particles depends on the kinetic energy of the particles.

When kinetic energy of the particles is 100%, the particles can oscillate from x₁ to x₅.

However, when the total energy of this particles is reduced to one-third (¹/₃) or 33% of the initial energy of the particle, the oscillation of the particles will be reduced.

• The maximum position the particle can oscillate is x₅

• The half position the particles can oscillate is x₃

Since 33% is less than the half of the energy of the particle, the particle will oscillate between x₁ and x₂.

Thus, we can conclude that the particles can undergo small oscillations around x₂.

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