SOLUTION: An object moves in simple harmonic motion described by the equation d=5 cos pit, where t is measured in seconds and d in inches. Find the following.
a. the maximum displacement
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a. the maximum displacement
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Question 1171811: An object moves in simple harmonic motion described by the equation d=5 cos pit, where t is measured in seconds and d in inches. Find the following.
a. the maximum displacement
b. the frequency
c. the time required for one cycle
I need to find a,b,c Answer by math_tutor2020(3817) (Show Source):
Comparing that last equation to the form , we have:
A = 5
B = pi
C = 0
D = 0
Note: we won't be using the values of C and D for this problem (they handle horizontal and vertical shifting).
The value of A determines the amplitude. We have |A| = |5| = 5 as our amplitude which is the maximum displacement. The object moves up and down, going at most 5 inches above or below its initial position. I recommend graphing to see this.
The value of B will help us find the frequency. First we compute the period T
T = 2pi/B
T = 2pi/pi
T = 2
The period is 2 seconds. This means every 2 seconds, the cycle repeats itself. In other words, the length of each cycle is 2 seconds.
The frequency f is 1 over the period, aka the reciprocal of the period.
frequency = 1/(period)
f = 1/T
f = 1/2
f = 0.5
The frequency is 1/2 = 0.5 cycles per second. Every second, the object completes half a cycle. Note how the units for T are in "seconds per cycle". When we apply the reciprocal, the units swap getting "cycles per second".
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