Final answer:
The amplitude of a damped oscillator with an initial amplitude of 18cm and a damping factor of 5.0% per oscillation would be approximately 4.97cm after 23 oscillations.
Step-by-step explanation:
The student has inquired about a damped oscillator, which is a physics concept related to simple harmonic motion. Specifically, they have a mass of 500g (0.5kg) attached to a spring that oscillates with a period of 0.50s. With a damping factor that decreases the amplitude by 5.0% each complete oscillation, we can calculate the amplitude after 23 oscillations using an exponential decay formula.
The initial amplitude is given as 18cm, and to find the amplitude after 23 oscillations, we use the formula A(n) = A(0) * (1 - damping_factor)^n, where A(n) is the amplitude after n oscillations, A(0) is the initial amplitude, and the damping_factor is 0.05 (representing the 5.0% decrease).
Therefore, after 23 oscillations, the amplitude would be:
A(23) = 18cm * (1 - 0.05)^23
A(23) = 18cm * (0.95)^23
A(23) = 18cm * 0.276
A(23) = 4.97cm (approximately)
The amplitude after 23 oscillations would approximately be 4.97cm.