The displacement of an object in SHM is given by y(t) = (7.0 cm)sin[(1.58 rad/s)t]. What is the frequency of the oscillations?
1
The frequency of the oscillations can be determined from the angular frequency, which is given by:
ω = 1.58 rad/s
The frequency is then given by:
f = ω/2π
Substituting the value of ω, we get:
f = 1.58/2π ≈ 0.251 Hz
Therefore, the frequency of the oscillations is approximately 0.251 Hz.
To find the frequency of the oscillations in Simple Harmonic Motion (SHM), we need to recall the formula for the displacement of an object in SHM, which is given by:
y(t) = A * sin(ωt)
Where:
- y(t) is the displacement of the object at time t,
- A is the amplitude of the oscillations (in this case, 7.0 cm), and
- ω is the angular frequency of the oscillations.
We can see that the angular frequency ω is given by the coefficient in front of t inside the sine function.
Therefore, in the given equation y(t) = (7.0 cm) * sin[(1.58 rad/s)t], the angular frequency is 1.58 rad/s.
Now, to find the frequency of the oscillations, we can use the relationship between angular frequency (ω) and frequency (f):
ω = 2πf
Rearranging this equation to solve for f, we have:
f = ω / (2π)
Plugging in the given angular frequency, we can calculate the frequency of the oscillations as follows:
f = 1.58 rad/s / (2π) ≈ 0.251 Hz
Therefore, the frequency of the oscillations is approximately 0.251 Hz.