The position of some object moving along the x-axis is observed to be x(t)=9cos(pi*t/3+pi/4) meters. Find the frequency.
(pi t/3) is all that matters. I assume t in seconds.
at t = 0 that is 0
when is it 2 pi?
pi T/3 = 2 pi
T = 6 seconds period
f = 1/T = 1/6 Hz
To find the frequency of the object in motion, we need to analyze the given equation x(t) = 9cos(pi*t/3 + pi/4).
In general, the equation of a cosine function is of the form:
y = A * cos(B * (x - C))
Where:
A is the amplitude of the function,
B is the frequency of the function (measured in radians),
C is the phase shift of the function.
Comparing this general form to the given equation, we can see that:
Amplitude (A) = 9
Frequency (B) = pi/3 (coefficient of 't' inside the cosine function)
However, note that the frequency in radian measure represents the number of cycles or oscillations that occur in 2π radians (a full circle).
Let's convert the frequency from radian measure to cycles per second (or Hertz).
1 cycle corresponds to an angle of 2π radians, so the frequency in cycles per second can be calculated by dividing the given frequency in radians by 2π.
Frequency (f) in Hertz = (pi/3) / (2π)
Simplifying, we get:
f = (pi/3) / (2π)
f = (pi/3) * (1 / (2π))
f = 1 / 6
Therefore, the frequency of the object's motion is 1/6 Hertz.