Lab Problems with Simple Harmonic Motion in Springs

[jallison]

Homework Statement

During lab we measured the amount a spring was stretched when various masses where hung on it to verify Hooke's Law. We started with a 50 gram mass and then increased with 50 grams up until 350, for seven measurements. We then graphed the force and displacement. The lab manual says that the slope is k, the spring constant ( with force on the y-axis and displacement on the x-axis).
When we did this we only got a slope of 0.1 meter.

We were then asked to find the period of oscillation. We used a stopwatch to time 20 oscillations for three different masses. Then we used the equation T=2∏√M/k
T is the time for the period, M is the mass and k is the spring constant
However our numbers were no where near the actual value. They didn't even make since. Obviously it doesn't take 7 seconds to oscillate. The final step was to determine the effective mass of the spring and to consider that in the calculation for the oscillation time as well, which only made our numbers even more off. What could have went wrong.

Homework Equations

T=2∏√M/k
T is the time for the period, M is the mass and k is the spring constant

The Attempt at a Solution

The measured time for osculation with a 50 gram weight attached was 0.7155 seconds. That is approximately what I get when I take √M/k, before multiplying by 2∏.

The measured time with 150 g was 0.95s. When I used the equation I got 7.7s.

The only thing I can think of is that the k is wrong. Everything else are constant numbers. I substituted 0.7155s into the equation and came up with k=3.855, but I have been back over my numbers in the first section and cannot see where something when wrong there.

The initial, resting length of the spring was 28.2 cm. With each trial a 50 gram weight was added. Displacement in meters were 0.043; 0.091; 0.144; 0.196; 0.249; 0.297; and 0.348.

We asked the graduated assistant that teaches our lab, but he said he did not know what we did and was really rude to us (like always). He said our graph looked good so he didn't know. Our final is Tuesday and I still have to write the lab report for this lab. Please, help me out if you know what we did wrong.

Thanks!

 

[Stonebridge]

I calculate a different value for the slope.
Have you remembered to
-make sure the mass is in kg
-multiply mass by g to calculate the force?

The value of k must be in units of Nm^-1
Your answer being out by a factor of about 10 is the clue.

 

[jallison]

I thought this is what I did as far as the first part. For example, I had 0.50kg * 9.8m/s²= 0.49N.

I am not sure that I understand the second part where k needs to be in Nm^-1. Can you explain that to me?

 

[Stonebridge]

I thought this is what I did as far as the first part. For example, I had 0.50kg * 9.8m/s²= 0.49N.

I am not sure that I understand the second part where k needs to be in Nm^-1. Can you explain that to me?

50 gram is 0.05kg not 0.5 kg

There is the factor of 10 you have lost in the calculation of the slope.

The slope, k, is force divided by extension. This is Newton divided by meter

 

[asteriatic]

It sounds like there may have been some errors in your experimental setup or measurements that could have affected your results. First, it is important to make sure that the spring is being hung vertically and that the weights are being added evenly and not causing the spring to tilt or twist. This could lead to inaccurate readings and a incorrect calculation of the spring constant.

Additionally, it is possible that the stopwatch was not started and stopped accurately, leading to incorrect measurements of the period of oscillation. It may be helpful to use a digital timer or have multiple people time the oscillations to ensure more accurate results.

Another factor to consider is the accuracy of the equipment being used. If the spring is not a perfect Hooke's Law spring, it may have a slight variation in its spring constant which could affect your results. It is also important to make sure that the weights being used are accurate and consistent.

In terms of the discrepancy in your calculated period of oscillation, it is possible that there was a mistake in your calculations or in recording the measurements. It may be helpful to recheck your work and have someone else review it as well.

Overall, it is important to carefully follow the experimental procedure and double check all measurements and calculations to ensure accurate results. If you continue to have trouble, it may be helpful to consult with your lab instructor or a classmate for further guidance. Good luck on your lab report!