An 0.90 kg object is attached to one end of a spring, and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown in the drawing. With the aid of these data, determine the following values.
I got a,b,d,e right.
for C, I used:
ω = k / m . Solving for k we find
k = ω
2m = (1.6 rad/s)
2
(0.90kg) = 2.30 N/m
but Webassign is telling me that I got it wrong.
i got 1.6 from ω =2π/T
=
2π/4.0 s
= 1.6 rad/s
(From the graph, the period is T = 4.0 s)
Well, it seems like you're having a little trouble with the question. Don't you worry, it happens to the best of us! Let me help you out with the answer.
In this case, the period T is indeed 4.0 seconds, which you correctly calculated from the graph using ω = 2π/T. However, there is a small mistake in your calculation for k.
Remember, the formula for the angular frequency ω in terms of the spring constant k and the mass m is ω = √(k/m), not ω = k/m. So we need to rearrange the equation to solve for k.
ω = √(k/m)
k/m = ω^2
k = mω^2
Using the given values, we have:
m = 0.90 kg
ω = 1.6 rad/s
Plugging these values into the equation, we get:
k = (0.90 kg) × (1.6 rad/s)^2
k = 2.3 N/m
So the correct value for the spring constant k is indeed 2.3 N/m. Give it another go and let's hope the Webassign clownliness level is reduced!
To calculate the spring constant, you need to use the formula:
ω = √(k / m)
Where ω is the angular frequency (2π / T), k is the spring constant, and m is the mass attached to the spring. From the given information, you correctly calculated ω = 1.6 rad/s.
Rearranging the formula, we get:
k = ω^2 * m
Plugging in the values, we have:
k = (1.6 rad/s)^2 * 0.90 kg
= 2.56 N^2/kg * 0.90 kg
= 2.30 N/m
So your calculation for the spring constant is correct. It seems there may be a mistake in the answer provided by Webassign.
To determine the value of C, which is the spring constant (k), you used the correct formula:
ω = k / m
In this case, ω represents the angular frequency, k represents the spring constant, and m represents the mass of the object.
You correctly found ω by using the formula ω = 2π / T, where T represents the period. From the graph, you determined that the period is T = 4.0 s, so you calculated:
ω = 2π / T
= 2π / 4.0 s
= 1.6 rad/s
This is the correct value of ω for this problem.
To solve for the spring constant k, you rearranged the formula ω = k / m and solved for k:
k = ω * m
= (1.6 rad/s) * (0.90 kg)
= 1.44 N/m
According to your calculations, the spring constant (k) is 1.44 N/m.
If Webassign is indicating that your answer is incorrect, double-check your calculations to ensure you didn't make any calculation errors. Additionally, verify that you entered the answer in the correct format or units as required by the platform.