In simple harmonic motion, the maximum displacement is 4 inches, the frequency is 4.71 Hz, and the time required for one cycle is approximately 0.84 seconds.
Step-by-step explanation:
In simple harmonic motion, the displacement is given by the equation x(t) = X cos(2πt), where X represents the maximum displacement or amplitude.
Therefore, in the given equation d = -4 cos(3π/4t), the maximum displacement is 4 inches.
The frequency of motion can be determined by analyzing the coefficient in front of 't' in the equation. In this case, it is 3π/4, which indicates that the motion completes 3π/4 cycles in 1 second. Therefore, the frequency is (3π/4) cycles per second or approximately 4.71 Hz.
The time required for one cycle can be determined by finding the period, which is the inverse of the frequency. So, the period in this case is (1/(3π/4)) seconds or approximately 0.84 seconds.