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General Physics – PH212Your Name: _____________________________Lab#6 – Damped Harmonic Oscillator and Travelling WavesMay 15, 2020Group Members’ 1st Names ____________________________Please submit one pdf lab report to gradescope for the group, gaadescope will ask for names of lab partners. Please don’t forget to write your lab partner’ names on the lab report.ObjectiveIn this experiment you will explore the properties of the damped harmonic oscillator. How the amplitude of a damped oscillator decays exponentially. You will also explore the properties of travelling waves and their behavior different media.Pre-Activity for Damped Harmonic OscillatorDo the following derivations or predictions before conducting the actual experiment.Write the equation of motion for a damped harmonic oscillator. Identify each quantity used in the equation. (Note you don’t have to derive the equation).Write the equation for angular frequency of the damped oscillator. Again identify the quantities in the formula.What is the time constant defined for the damped oscillator and the formula used for it?EquipmentThis lab uses the Masses and Springs simulation from PhET Interactive Simulations at University of Colorado Boulder, under the CC-BY 4.0 license: 1: Finding the Spring ConstantProcedureOpen the “Lab” screen. Explore the site and familiarize yourself with the screen. Test all the buttons and see what they mean.Choose the largest setting for spring constant.Use the “displacement/ natural length” option setting to make measurement of displacement easier. Attach a 200g mass and measure the displacement, and then a 300g and measure the displacement. Record the data and calculate spring constant from each mass and average the values. Don’t forget mass is not a force.Activity 2: Finding amplitude of a damped oscillatorTo obtain good data for this part you need to decide with your group how you will perform the experiment. Please be patient; you will collect good data. You need to measure the displacement of the of the oscillation for several seconds for every 0.20 sec or around this interval. You may follow the steps below as guideline. You can also brainstorm a method that works better for you.Choose the following settings: keep spring constant as the largest value same as activity 1; the damping on first notch (lowest), choose period trace and mass equilibrium.Use the ruler to measure displacements. Choose the slow motion, and stopwatch to measure time. Set play of motion to pause and set the stopwatch to take the time (all are frozen till you play the motion, or step the motion forward.Attach a 300 gram mass to the spring and move it up as far as possible (if motion is on pause, mass will stay still at its amplitude). Measure this displacement and record it for t = 0 in a table. Make a large table for time in second and displacement in meters. Play the oscillation for 5 complete oscillation to determine the period of the oscillation. You can also put it on pause and step it through 5 periods. Record the value in data section of your lab. Put the play on pause and reset the clock and activate it to be ready. Again, place the mass at highest point. Step the motion and make displacement measurement every 0.15sec. Keep time continuous (don’t reset the stopwatch throughout the experiment). Also stop at every positive and negative amplitude to measure the time at amplitudes as well. Record the times and corresponding displacement in the table. Note: displacements below equilibrium line are negative. Continue the measurements in the same way for at least 5 periods. After that continue measurement but only for amplitudes for an additional 5-8 periods. More is better. Make a separate table for time and amplitudes.Make a separate table for time and positive amplitudes and another one for time and negative amplitudes. Data Analysis for Activity 2:You have three table of values, one showing time and displacement for at least five periods (includes time of amplitudes too). The other table is time and all positive amplitudes from t =0 and the third one is time and Negative amplitudes.Plot on the same grid displacement vs, time and both positive and negative amplitudes vs. time. Choose scatterplot with smooth curve. If you have collected good data, you will have a decaying oscillation enveloped between two exponential curves. Submit the graph.Fit an exponential curve only to the graph of positive Amplitudes vs, time and display its equation. Read the period of the oscillation from graph. Best is to read for several period and take average for the period of damped harmonic oscillator. How does the period compare to the period you measured in part D of activity 2. Calculate the angular frequency from the period. Compare the amplitude of the equation of damped oscillator (See item 1 of your pre-activity) to the equation of your exponential curve fit. What does the exponent of the curve fir represent?From the value of exponent and mass of the oscillator, calculate the damping constant b.Use your calculated value of damping constant, and your known quantities to calculate the angular frequency of the oscillation. Compare it to the value you obtained part 5) above. Consider item 5) as actual value and calculate % error; discuss sources of errors.From your graph decaying amplitude read the first time constant as closely as you can. From that and the damping constant (item 6) above) calculate the oscillating mass and compare it to the actual mass (300 grams). Calculate again a percent error and comment on the errors.Summary/ Conclusion and reflection for Activity 2Activity 3 – Travelling wavesPre-activity: Prior knowledge A) In your words, define what a transverse wave is: B) Give an example from your own experience that you know is a transverse wave. C) For your own example, which physical parameters do you think determine the speed of the wave? A) In your words, define what a longitudinal wave is: B) Give an example from your own experience that you know is a longitudinal wave. C) For your own example, which physical parameters do you think determine the speed of the wave?Activity 3: Explore transverse waves Develop your understanding: 339090040513000Open Waves on a String, \Then investigate wave behavior. As you explore, think about how you would describe waves and some reasons the waves might act the way they do. Explain your understanding: Write a list of wave characteristics to describe the waves (see your notes from Wed lecture). Describe each characteristic in your own words so that any person could understand waves. Use images to help with the descriptions.Tips: Later during this lab, you will relate your own descriptions to scientific ones. It is important that you have your own words to begin your learning, so rely on your language and do not research vocabulary in the textbook or on the computer. Also, learning is best when you make your own drawings. Perhaps you can?insert images of your own drawings. If you cannot do this then use images from “Waves on a String” that look like your drawings.Activity 3- continued : Expand your understanding: For steps 2-3 Investigate waves with? Oscillate and No End? Tips: Helpful tools and Use the Amplitude slider, and see the changes you notice. Answer the questions; include imagesDefine Amplitude in everyday language.?Explain how the wave behaves as the Amplitude changes using the characteristics you described in 1, like how does frequency, wavelength, speed, … change as you change amplitude)Use the Frequency slider. Answer the questions; include images.Define Frequency in everyday language.Explain how the wave behaves as the Frequency changes using the characteristics you described in 1)Use the Tension slider. Answer the questions; include images. Define Tension in everyday language.?Explain how the wave behaves as the Tension changes using the characteristics you described in 1)Summary and Conclusion/ reflection for travelling waves ................
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