A buoy oscillates in simple harmonic motion according to the motion of waves at sea. An observer notes that the buoy moves a total of 6 feet from its lowest point to its highest point. The buoy returns to its highest point every 15 seconds.
Amplitude: 6 feet
Period: ???
Frequency: ???
Possible equation:???
Period = time per cycle = 15 seconds
frequency = 1 / period = 1/15 hz
amplitude= 3 ft because its actually the distance from the center to each side.
from there just put it into standard form.
Would I use cosine or sine?
It doesn't make a difference as long as your value for when t = 0 is correct since sin is just cosine phase shifted by pi/2.
Cosine is probably easier in this case because then you wont need to do a shift.
nevermind I thought it said that it began at its highest point.
Since they didn't specify any initial conditions you're free to use either sin or cosine with no phase shift.
How do I find omega (ω)?
w = 2*pi*period
To find the period and frequency of the buoy's motion, we need to understand the basic properties of simple harmonic motion.
1. Amplitude: The amplitude of a wave or oscillation is the maximum displacement of the object from its equilibrium position. In this case, the amplitude is given as 6 feet, which means the buoy moves 6 feet from its lowest point to its highest point.
2. Period: The period of a wave or oscillation is the time it takes for one complete cycle or one full oscillation to occur. In this case, the buoy returns to its highest point every 15 seconds. Therefore, the period is 15 seconds.
Calculating Frequency:
Frequency (f) is the number of cycles or oscillations per unit of time. It can be calculated using the formula f = 1 / T, where T is the period. Therefore, the frequency of the buoy's motion is 1 / 15, which simplifies to 0.067 Hz (approximately).
Calculating Equation:
The basic equation of simple harmonic motion is given by x(t) = A * cos(2πf * t), where x(t) represents the displacement of the object at time t, A is the amplitude, f is the frequency, and t is the time.
In this case, the equation for the buoy's oscillation can be written as x(t) = 6 * cos(2π * 0.067 * t).
So, the period of the buoy's motion is 15 seconds, the frequency is 0.067 Hz, and the possible equation is x(t) = 6 * cos(2π * 0.067 * t).