Homework SourseA buoy oscillates in simple harmonic motion as waves go past
A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 14 feet from its high point to its low point, and it returns to its high point every 8 seconds. Write an equations that describes the motion of the buoy, where the high point corresponds to the time t = 0. H(t) =??
A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 14 feet from its high point to its low point, and it returns to its high point every 8 seconds. Write an equations that describes the motion of the buoy, where the high point corresponds to the time t = 0. H(t) =??
Solution
The amplitude is given by half the distance from the low point to the high point.
Here low to high distance is given as 14 feet
So, Amplitude=14/2=7ft
Now, it is given that the period of oscillation is 8sec
so w can be found by using the formula w=2pi/period
w = 2pi / 8 = pi / 4.
The equation of motion with y in ft. and t in sec.is given by:
y=Acoswt
here y=H(t) and w=pi/4
So,
H(t)= 7 cos(pi / 4)t
