Final answer:
The amplitude of a simple harmonic oscillator cannot be determined with the given data. The amplitude is greater than the current displacement since the acceleration is opposite to the displacement and is maximized at the amplitude. Thus, the correct answer is option 4) Cannot be determined.
Step-by-step explanation:
When an object is undergoing simple harmonic motion (SHM), we can determine its amplitude by examining the relationship between displacement, velocity, and acceleration at a particular moment. Given that the object has a displacement of 0.555 m to the right of its equilibrium position, a velocity of 2.25 m/s to the right, and an acceleration of 8.30 m/s² to the left, we can use the fact that the maximum acceleration in SHM happens at the amplitude. The equation linking acceleration (a) to displacement (x) is a(t) = - (k/m) × x, where k is the spring constant and m is the mass of the object. Without knowing k or m, we can qualitatively analyze that since acceleration is maximized at the amplitude and is currently to the left (opposite of the displacement), while the object is moving to the right (indicating it hasn't reached the turning point), the current displacement is not at its maximum value. Therefore, the amplitude must be greater than 0.555 m. Given the options provided, the precise value of the amplitude cannot be determined with the information given; the correct answer is option 4) Cannot be determined.