The displacement of an object in SHM is given by y(t) = (7.1 cm)sin[(1.64 rad/s)t]. What is the frequency of the oscillations in Hz?
I'm completely stuck here. I was thinking that frequency = 1/t. I'm stuck with the information given. Please help!
The 1.64 rad/s number in front of "t" is the ANGULAR frequency, w. The frequency in cycles per second (Hz) is w/(2 pi), or 0.261 Hz.
Thank you so much! I wasn't understanding the format.
To determine the frequency of the oscillations, we need to use the formula:
f = 1/T
where f is the frequency in Hz and T is the period of oscillation in seconds.
In the given equation, y(t) = (7.1 cm)sin[(1.64 rad/s)t], we can observe that the angular frequency, ω, is given as 1.64 rad/s. The angular frequency is related to the period by the equation:
ω = 2πf
Rearranging the equation, we get:
f = ω/(2π)
Substituting the given angular frequency, we have:
f = 1.64 rad/s / (2π)
Calculating the value, we find:
f ≈ 0.261 Hz
Therefore, the frequency of the oscillations is approximately 0.261 Hz.