A weight is attached to a spring that is oscillating up and down. it takes 3 sec. for the spring to complete one cycle, and the distance from the highest to lowest point is 4 in. What equation models the position of the weight at time t seconds?
a. y=2sin[pi/3(t)]
b. y=4sin[pi/3(t)]
c. y=2sin[2pi/3(t)]
d. y=4sin[2pi/3(t)]
e. y=2sin[3pi(t)]****
f. y=4sin[3pi(t)]
I does 2 pi radians in a period
well sin 2pi t/T is sin 2 pi t/3
amplitude = 2
so
2 sin 2 pi t/3
I choose c
Correct
The correct equation that models the position of the weight at time t seconds is:
e. y = 2sin[3π(t)]
To find the equation that models the position of the weight at time t seconds, we need to identify the characteristics of the motion:
1. The amplitude of the oscillation is the distance from the highest to lowest point, which is 4 inches. This means the coefficient of the sine function should be 4.
2. The period of the oscillation is the time it takes for one complete cycle, which is 3 seconds. The period is inversely proportional to the coefficient of t inside the sine function. So, if the period is 3 seconds, the coefficient of t inside the sine function should be 2π/3.
Combining these characteristics, the equation that models the position of the weight at time t seconds is y = 4sin[(2π/3)t].
Therefore, the correct option is e. y = 2sin[3π(t)].