A weight is attached to a spring that is oscillating up and down it takes 6 sec for the spring to complete one cycle and the distance from the highest to lowest point is 7 in what equation models the position of the weight at time t seconds.
a. y = 7sin ( (pie / 3)t)
b. y = 7sin ( (pie / 6)t)
c. y = 7sin (6(pie)t)
d. y = 3.5sin ( (pie / 6)t)
e. y = 3.5sin ( (pie / 3)t)
f. y = 3.5sin (6(pie)t)
I think that its e but I am not sure
mmm I could go for a good pecan pie right now.
That's pi, not pie! Grrr. Pie is what you eat.
The period is 6, so you start with y = sin(π/3 t), so the only choices are A and E
The amplitude is 3.5, so that makes it E.
Ans: E I did it
Well, oscillating springs can be quite funny. So, let me help you solve this with a touch of humor.
If the spring takes 6 seconds to complete one cycle, that means it goes from the highest to the lowest point and back in that time. The distance from the highest to the lowest point is given as 7 inches.
Now, let's consider your options.
a. y = 7sin((π/3)t): Pie might be delicious, but in this equation, something seems off. It's not accounting for the full 6 seconds it takes for one cycle. Not the right answer, my friend.
b. y = 7sin((π/6)t): Ah, this one seems interesting. It takes into account the 6 seconds for a complete cycle. Could this be the right answer? Let's keep going.
c. y = 7sin(6πt): 6π, six times the circumference of a pie we had earlier. However, it seems to ignore the distance from the highest to the lowest point being 7 inches. That doesn't seem to fit the bill.
d. y = 3.5sin((π/6)t): Ah, a twist! This equation takes into account the 7 inches from highest to lowest point and has the correct time for a full cycle. Hmm, could this be it?
e. y = 3.5sin((π/3)t): It seems this equation has the same issue as option a, missing the full cycle time of 6 seconds. Not the answer we're looking for.
f. y = 3.5sin(6πt): Oh dear, it's the same issue as option c. This equation isn't capturing the distance of 7 inches.
So, after a humorous analysis, it appears that option d, y = 3.5sin((π/6)t), seems to be the most fitting equation for the position of the weight at time t seconds.
To determine the equation that models the position of the weight at time t seconds, we should analyze the given information about the oscillating spring.
In a simple harmonic motion of a mass-spring system, the equation that represents the position (displacement) of the weight as a function of time is given by:
y = A * sin(ωt + φ),
where:
- y is the displacement of the weight from the equilibrium position,
- A is the amplitude of the oscillation (the distance from the highest to lowest point),
- ω is the angular frequency (2π divided by the time period, T),
- t is the time in seconds, and
- φ is the phase constant or initial phase angle.
We are given that the time period (T) is 6 seconds and the amplitude (A) is 7 inches.
Calculating the angular frequency (ω):
ω = 2π / T = 2π / 6 = π / 3.
So far, we have:
y = 7sin( (π/3)t + φ).
To find the value of the phase constant (φ), we need more information. The phase constant represents the initial position of the oscillating weight at a certain time (usually taken at t = 0).
Without any additional information about the initial conditions, we cannot determine the exact value of φ. However, if we assume that the oscillation starts at the highest point (maximum displacement), then when t = 0, the term π/3 * 0 + φ equals zero (the sine of zero is zero). This means that the phase constant φ = 0.
Thus, the final equation that models the position of the weight is:
y = 7sin((π/3)t).
Comparing this equation to the given options, we can see that the correct answer is option (e):
y = 3.5sin((π/3)t).
Therefore, you were correct in choosing option (e).