Final answer:
The average kinetic energy of a simple harmonic oscillator with mass m, angular velocity ω, and amplitude A is (1/4)m(ωA)², calculated by taking half of the maximum kinetic energy since the energy oscillates between kinetic and potential forms.
Step-by-step explanation:
The average kinetic energy of a simple harmonic oscillator during one time period can be determined by considering both the kinetic and potential energy of the system, as the total energy remains constant. For a simple harmonic oscillator with mass m, angular velocity ω (omega), and amplitude A, the maximum kinetic energy is reached when the potential energy is zero, which happens at the equilibrium position (x=0). The maximum kinetic energy at this point is given by the expression (1/2)m(ωA)². However, the average kinetic energy over one period would be half of this maximum value since the kinetic energy fluctuates between zero and the maximum value as the oscillator moves. Therefore, the average kinetic energy over one period for a simple harmonic oscillator is (1/4)m(ωA)².