Minnesota State University Moorhead From the SelectedWorks of Beau v Scheving

Transcription

1 Minnesota State University Moorhead From the SelectedWorks of Beau v Scheving Fall August 21, 2012 Damped Pendulum Beau v Scheving, Minnesota State University - Moorhead Available at:

2 Measuring the damping effects on a pendulum Beau Scheving By: Beau Scheving Objectives & Intro The objective of this experiment is to find out the effects a magnetic gate would have on a swinging pendulum. We will be changing the amount of effect the magnetic gate has on the pendulum by changing the distance in between the magnetic poles increasing the magnetic field that the pendulum has to go through. The measurement that we will be making throughout our experiments will be the OP (oscillation period) f (Frequency) T (tau / dampening constant) and Xb ( Distance between gate). The Setup Equipment needed - Rod Stand - Rotary Motion Sensor - Magnetic Gate - Pendulum You will first take the rod stand and up the rotary motion sensor to it. Then plug it into logger pro so we can see and graph the measurement. Then you attach the pendulum to the rotary sensor. After place the magnetic gate directly below the pendulum and adjust the pendulum till it is directly in the middle of the magnetic gate. This can be seen in the Diagram 1 below. Diagram 1

3 Experiment Beau Scheving To start out the experiment we want to know how much a magnetic gate would effect a pendulum. So, first we had the pendulum go for 20 seconds with no magnetic gate to see how it dampens naturally. After 20 seconds we have our results graphed on logger pro. After we have all the date we try to get a curve to fit our graph so we can get numerical results. After a while we found the equation (1.1) that worked. A*e^(k*t)*sin(Bt+C)+D (1.1) Where A is amplitude t is our respect to time and k which is our decay constant. After we got all of that we are able to find out OP, f, and T. We measured the distance between to peak to find out OP in seconds. Then we used the equation (1.2) to find f. OP=1/f (1.2) Then from our curve fit we are able to find our k. We use that k to find our Tau shown in equation (1.3) Graphed results shown below on Graph 1 k=1/t (1.3) Graph 1 After we have got all of our measurements for our pendulum with no damping we repeated this process 3 more times. The only difference is that we put in the magnetic gate. The first of the 3 the gate was 2.5cm (±.1) apart. When we did this we say a graph much like the one above, but with some slite differences. We notice that this pendulum has dampened

4 Beau Scheving more then the one without the magnetic gate. This was good to see because it is what you would expect to see. The 2 nd we put the gate at 2cm (±.1) and the 3 rd was at 1.5cm (±.1). In both of these two we see the same case where the graphs look similar with more dampening. No after we have all of our data we want to see what effects do these measurements have with each other. So in Table (1.1) we graphed our results of T (±.5 s) (y-axis) compared to our Xb (±.1 cm) (x-axis). We decided to use T and Xb in this first graph because they are directly related. (Note that we put the distance of our magnetic gate at 10cm for our graph with no magnetic gate. This is there just to help make our plot fit) Table (1.1) You can see in this graph as the magnetic gate gets closer and closer the smaller T is therefore has a quicker dampening. In this 2 nd graph we wanted to graph two measurements that are not directly related. So for Table (1.2) we decided to graph T compared to our OP.

5 Beau Scheving Table (1.2) In this graph you can see that the T goes up consistently with OP. Results So we found that just by measuring a pendulum you can easily find its OP, f, and T. We found out that using these measurements you can find the dampening of the pendulum. So this experiment showed that as you make the distance between the magnetic gate smaller that is has more effect on the pendulum and therefore it cause the pendulum to dampen faster.