To determine the displacement of a particle undergoing simple harmonic motion, we need to know the amplitude, frequency, and time. In this case, the given values are:
Amplitude (A) = 5.0 cm Frequency (f) = 20 Hz Time (t) = 0.040 seconds
The equation for the displacement (x) of a particle in simple harmonic motion as a function of time is:
x = A * cos(2πft)
Substituting the given values into the equation, we have:
x = 5.0 cm * cos(2π * 20 Hz * 0.040 s)
Calculating the expression within the cosine function:
2π * 20 Hz * 0.040 s ≈ 5.03
x ≈ 5.0 cm * cos(5.03)
Using a calculator or math software to find the cosine value, we can determine the displacement:
x ≈ 5.0 cm * (-0.617)
x ≈ -3.085 cm
Therefore, at 0.040 seconds after passing its equilibrium position, the particle has a displacement of approximately -3.085 cm (moving in the negative direction).