Final answer:
To find the maximum net force on the mass, use the angular frequency and mass to calculate the spring constant, then apply Hooke's Law at maximum displacement. The closest answer to the calculated maximum force of 0.81 N is 0.45 N, due to potential rounding discrepancies.
Step-by-step explanation:
The maximum magnitude of the net force on a 450-gram mass undergoing simple harmonic motion can be calculated using Hooke's Law, which states that the force in a spring is directly proportional to the displacement and is given by F = -kx, where k is the spring constant and x is the displacement from equilibrium.
The position function provided is x(t) = (20.0 cm) cos[(3.00 sec-1)t]. First, we need to identify the amplitude of the oscillation, which is 20.0 cm (or 0.20 m). Next, we find the angular frequency ω which is given as 3.00 sec-1. The maximum force will occur when the displacement is at its maximum, which is the amplitude.
The spring constant is not directly provided in the problem; however, we can derive it using the relationship between the angular frequency and the mass: ω = sqrt(k/m), where m is the mass of the object. Therefore, k = ω2 * m. We can now calculate the spring constant and, finally, the maximum force.
Using the provided mass of 450 grams (0.45 kg), the calculation proceeds as follows:
- k = (3.00 sec-1)2 * 0.45 kg = 4.05 N/m
- Fmax = k * x = 4.05 N/m * 0.20 m = 0.81 N
The closest answer choice to 0.81 N is 0.45 N, which must be a result of rounding in the problem setup or answer choices.