Simple Harmonic Motion

Transcription

1 Simple Harmonic Motion Abstract The objective of this first lab are to learn the use of the computerized Science Workshop interface for data acquisition and to study the simple harmonic motion of a mass-spring system. 1 Material Stand Universal clamp Horizontal rod Large spring Hooked weights 500 Interface Force sensor Motion sensor Stopwatch 2 the Computer Interface setup 1. Connect the 500 Interface to the computer via the USB cable. Make sure it is also connected to the power cord, plugged in and switched on (you should see a green light on the front). Figure 1: The Pasco 500 Interface 2. Start the CAPSTONE software by double clicking the Capstone icon on the desktop. Figure 2: Capstone Icon Rémi Poirier page 1 of 5

2 Figure 3: The Pasco 500 Interface 3. Once the program has opened, select "Table & Graph". 4. On the left bar, click "Hardware Setup". You should see a picture of the 500 Interface. Figure 4: Select Hardware setup from the left hand side. 5. Click "Add Sensor/Instrument" and select the sensor you are using. If you are not sure if it is digital or analog, ask your teacher. 6. If it is setup correctly, you should see the sensor(s) that you are using with green lines pointing to the ports where the sensors are attached to. Figure 5: Green lines are shown when the Interface communicates with the sensors. 7. Plug in your sensors to the correct ports on the 500 Interface. 8. You are now ready to acquire data. Rémi Poirier page 2 of 5

3 Figure 6: Setting up the graph. 9. Select the data to appear on the x and y axes of the graph using the "select Measurement" pull-down menus. 10. To start recording data use the "Record/Stop" button on the bottom of the screen. Figure 7: Use the Record/Stop button to acquire data. 3 Data Acquisition 1. Record the position of the mass when it is not moving. This is called the equilibrium position of the vertical mass-spring system. If possible calibrate the motion sensor to read ZERO at that position. Use the hardware setup section for this sensor. 2. Stretch your spring-mass system and release it. It will start to oscillate up and down. WARNING: Make sure the mass doesn t bounce off the spring and fall on the motion sensor, you could damage the device. Always place the protection mesh over the motion sensor when performing this experiment. 3. With the computer interface, record the motion of the mass as a function of time for at least 5 periods. One period is the time necessary for the mass to come back to the same position, and move in the same direction. Rémi Poirier page 3 of 5

4 Figure 8: Diagram of the setup. 4. Export the data to a Comma Delimited File (.CSV). 5. In a spreadsheet software, import the.csv file, so that 4 columns are imported: (time(s), position(m), velocity(m/s), acceleration(m/s2). 6. Keep only data for 5 periods of the motion of the mass. 4 Analysis 4.1 position vs time graph 1. Plot a graph of the position as a function of time for your mass-spring system. Your graph should display five complete periods. Exceptionally, to display the data more easily you may use a scatter graph with the dots connected with a smooth curve. In Physics, we usually avoid connecting data points, unless it significantly helps, as in this case. Rémi Poirier page 4 of 5

5 2. Using the previous graph, calculate the period of the mass-spring system. Read the necessary information on the graph itself, and provide your answer with uncertainties. Reading from a graph is similar to using a ruler, the positions have an uncertainty due to the chosen scales of the graph. 3. What is the amplitude of the motion? The Amplitude is defined as the largest distance from the equilibrium point. 4. Is the amplitude the same on both sides? 4.2 velocity vs time graph 1. Plot a graph of the velocity as a function of time. 2. What is the position of the mass when it is moving fastest? 3. What is the position of the mass when it is moving slowest? 4.3 acceleration vs time graph 1. Plot a graph of acceleration as a function of time. 2. What is the position of the mass when it feels the largest acceleration? 3. What is the position of the mass when it feels the smallest acceleration? 4.4 acceleration vs position 1. Plot a graph of acceleration as a function of position. 2. What are your observations. Rémi Poirier page 5 of 5