Final answer:
The frequency of the simple harmonic motion equation is 3/2.
Step-by-step explanation:
The frequency of a simple harmonic motion is given by the equation:
f = 1 / T
In the given equation, d = 2 sin(3π), the coefficient in front of sin represents the amplitude, not the angular frequency. So we need to find the period first to calculate the frequency. The period is given by:
T = 2π / angular frequency
Therefore, in this equation, the angular frequency is 3π, so the period is T = 2π / (3π) = 2/3. The frequency is the reciprocal of the period, so the frequency is f = 3/2.
The equation given is d = 2sin(3πt) where 3π is the angular frequency (ω). In simple harmonic motion (SHM), the frequency (f) is related to the angular frequency by the formula ω = 2πf. Therefore, to find the frequency, we divide the angular frequency by 2π.
Given ω = 3π, the frequency f is calculated as f = ω / (2π) = 3π / (2π) = 3/2 or 1.5 Hz. Thus, the frequency of the simple harmonic motion is 1.5 Hz.