Final answer:
The maximum acceleration of a tuning fork executing simple harmonic motion can be found using the formula amax = A * ω², where A is the amplitude of the motion and ω is the angular frequency.
Step-by-step explanation:
The maximum acceleration of a tuning fork executing simple harmonic motion can be found using the formula:
amax = A * ω²
Where A is the amplitude of the motion and ω is the angular frequency. In this case, the frequency of the tuning fork is 1000 Hz, so the angular frequency is given by ω = 2π * f = 2π * 1000 = 2000π rad/s.
Therefore, the maximum acceleration is:
amax = A * (2000π)²
Substituting the given value of A = 0.4, we can calculate the maximum acceleration:
amax = 0.4 * (2000π)² ≈ 0.4 * 12,566,370 ≈ 5,026,548 m/s²