The function d=-8cos2t describes a simple harmonic motion, where d is the distance(in meters) an object travel in t seconds. What is the frequency?

for any y = a cos(kx) or y = a sin(kx)

the period is 2π/k

so for yours the period is 2π/2 = π

So there is one complete "motion" every π seconds

To find the frequency of a simple harmonic motion described by the function d = -8cos(2t), we need to understand the relationship between sine and cosine functions.

In a simple harmonic motion, the equation can be written as d = A cos(wt + φ), where A is the amplitude, w is the angular frequency, and φ is the phase angle.

Comparing this equation with the given function, we can see that the angular frequency (w) is equal to 2. However, we need to find the frequency (f), which is different from angular frequency.

The relationship between angular frequency and frequency is described by the formula:

f = w / (2π)

Substituting the value of w = 2 into the formula, we have:

f = 2 / (2π)

Simplifying, we get:

f = 1 / π

Therefore, the frequency of the simple harmonic motion described by the given function is 1/π, which is approximately 0.318 Hz.