The difference in energy between allowed oscillator states for the orangutan swinging in a tire is approximately 2.21 x 10^-34 J.
The difference in energy between allowed oscillator states can be found using the formula: ΔE = hf, where ΔE is the difference in energy, h is Planck's constant, and f is the frequency of the oscillation. In this case, the oscillation period is given as 3.00 s, so the frequency would be 1/3.00 Hz. Plugging these values into the equation, we get:
ΔE = (6.63 x 10^-34 J · s) × (1/(3.00 s)) = 2.21 x 10^-34 J
Therefore, the difference in energy between allowed oscillator states for the orangutan swinging in a tire is approximately 2.21 x 10^-34 J.