Final answer:
To fit angular position vs time data with a sinusoidal function, adjust the amplitude, angular frequency, and phase shift for an accurate model. The choice between sine and cosine depends on initial conditions.
Step-by-step explanation:
When fitting the angular position versus time measurements by a sinusoidal function, we use the general form x(t) = A cos(wt + φ), where A is the amplitude, w is the angular frequency, and φ is the phase shift. The amplitude A indicates the maximum displacement, the angular frequency w relates to the frequency of oscillation, and the phase shift φ accounts for any initial conditions that are not zero.
To fit experimental data, we adjust the amplitude, angular frequency, and phase shift to match the data points. For a block on a spring, the position data as a function of time might not start at the amplitude or with an initial velocity of zero, hence a phase shift is incorporated to accommodate this. The choice between using a sine or cosine function generally depends on the initial conditions; use cosine if the initial position is at the amplitude with zero initial velocity, and sine if the initial position is zero with maximum initial velocity.