Alessio Belaj
TA: Lei Fang

Lab Report 6
"Simple Harmonic Oscillations"

December 8th, 2016

Introduction:

Throughout this specific lab, our objective was to develop a deeper understanding concerning t he motion of a mass while connected to a spring . We were able to determine the spring constant by knowing the mass and seeing how it oscillated. By knowing the spring constant and certain equations we are able to make predictions relating to the period an d velocity. A real world application is using the spring constant to calculate the amount of springs needed to support an average human on a bed. Also, one would be that involved oscillation is when a person goes bungee jumping. So, as the bungee jumper ju mps, the elasticity of the cord causes the human to oscillate back and forth. This is a prominent example of oscillation in the real world.
Procedure:
Test for equilibrium by attaching a spring to bottom of the wood
Measure the distance from its lowest position to the table. Let it be delta( x)
Attach a 1000 kg mass to the spring, and measure the new distance from the spring's lowest position to the table .
Measure the spring constant (k)
Place the motion sensor directly above the hanging block .

Pull the block a little lower until feel it is a good distance.
Use LoggerPro to view the position, velocity, and acceleration vs time graphs.
Test the effect of varying mass on the period of oscillation by hanging different masses on the spring and allow them to oscillate by pulling down and releasing at a different position.
Observe the periods on the graph
By using a 200g mass, observe the effect of varying amplitudes on the period of oscillation by pulling down and releasing the mass at a different position.
Report Questions:
Describe how the mass moves relative to the equilibrium position.
When the mass is at equilibrium position, it begins to move at a steady pace. The acceleration is constant and the velocity is staying the same.
Calculate the maximum velocity from the position vs. time graph. Show your calculations. Compare with the value from the velocity time graph.
Vmax = (0.328m - 0.3597m)/(0.55s - 0.5s)
=0.634 m/s

At what position is the velocity a maximum?
The velocity is at maximum when the position is at equilibrium
Calculate the minimum velocity from the position vs. tim e graph. Show your calculations. Compare with the value from the velocity time graph.
Minimum velocity in this case would be the absolute value of the velocity, which is 0 m/s because at time = 0.2532 and the slope of the tangent = 0.

At what position is the velocity a minimum?
The velocity is a minimum at the highest (crest and trough) when the mass is changing the directions

Calculate the maximum acceleration from the velocity vs. time graph. Show your calculations. Compare with the value from the acceleration vs. time graph.
Maximum Acceleration= (0.177m - (-0.0099m))/(0.8s - 0.75s)
= 3.73 m/s^2
At what position is the acceleration a maximum?
The acceleration is at a maximum when the position is right as soon as the weight is s tretched and let go of. From that point, the acceleration will continue to decrease.

Conclusion:
As a conclusion, the results were as expected. As shown by the data and calculations, the force is directly proportional to the period of oscillation when tak ing the spring constant into account. There were a few sources of errors which could have prevented us from recording accurate data. One source of error was measuring the length of the neutral spring. It was difficult to measure the length of the spring ac curately because there were obstacles on the apparatus that prevented us from placing the ruler correctly. I have no suggestion, other than adjusting for human error such as time and position when releasing the mass on the spring.
More Graphs and Data: