A particle of mass 0.55 kg moves near x = 0 in U(x) = ½(18 N m⁻¹)x² + (39 J m⁻⁴)x⁴. Determine the small-amplitude angular frequency and period, and state why the quartic term can be neglected in this limit.

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ω = 5.72 rad s⁻¹; T = 1.1 s Near x = 0, the x² term dominates x⁴, so U ≈ ½kx² with k = 18 N m⁻¹. ω = √(k/m) = √(18/0.55) = 5.72 rad s⁻¹. T = 2π/ω = 1.1 s; the quartic contribution decreases faster than the quadratic contribution as x → 0.

Small oscillations in a potential well 3

A particle of mass 0.55 kg moves near x = 0 in U(x) = ½(18 N m⁻¹)x² + (39 J m⁻⁴)x⁴. Determine the small-amplitude angular frequency and period, and state why the quartic term can be neglected in this limit.

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