Harmonic Oscillator Homework: Graph, Spring Constant & Weight

[Karol]

Homework Statement

A test was made with a basket and 20 gram weights. they were put in the basket which hang on a spring, the basket was raised and released. the period was measured for a few number of weights in the basket. the results are as follows. the first of every pair is the number of weights and the second is the period in seconds:
(2, 0.53), (3, 0.60), (4, 0.66), (5, 0.72), (6, 0.77)
Draw a graph of T² as a function of the number of weights, n. comes out a straight line.
What is the spring constant and the weight of the basket.

Homework Equations

Period: $$T=2\pi\sqrt{\frac{m}{c}}$$

The Attempt at a Solution

From the above equation $$T^2=\frac{4\pi^2}{c}\cdot m$$
The slope $$\frac{4\pi^2}{c}$$ based on the last and first couples:
$\frac{4\pi^2}{c}=\frac{0.77-0.53}{(6-2)\cdot 0.02}=3\rightarrow c=13.2$
The spring constant c should be around 10[N/m]
The intersection with the T² axis: i take the first pair:
$0.53=3\cdot 0.04+B\rightarrow B=0.41$
I insert this B into: $$T^2=\frac{4\pi^2}{c}\cdot m$$
And get:
$0.41=3\cdot m_{basket} \rightarrow m_{basket}=0.14$
It should be around 30 grams

 

[rude man]

Not sure why you did what you did, so:

Your basic period is as you say, T = 2π√(m/k). (Use k instead of c. c is usually associated with damping).

But you realize that the basket has some mass also. So what is m actually?

Can you pick data points to solve for T (and incidentally the basket weight also)?

 

[dauto]

You forgot to square the periods.

 

[rude man]

You forgot to square the periods.

That part the OP already did.

The second part of the question was "What is the spring constant and the weight of the basket." The provided data was in T, not T²,

 

[dauto]

That part the OP already did.

The second part of the question was "What is the spring constant and the weight of the basket." The provided data was in T, not T²,

No, they didn't. They forgot to do it. Look at their calculation of the slope.

 

[rude man]

No, they didn't. They forgot to do it. Look at their calculation of the slope.

You're right, I saw the graph & thought they got it right. I should have read the part where they said they didn't!

Anyway, my response was to part 2 only.