For this week's problem set, you need to run a PhET simulation. "Founded in 2002 by Nobel Laureate Carl Wieman, the PhET Interactive Simulations project at the University of Colorado Boulder creates free interactive math and science simulations. PhET sims are based on extensive education research and engage students through an intuitive, game-like environment where students learn through exploration and discovery." - phet.colorado.edu On a web browser go to https://phet.colorado.edu/en/simulation/wave-on-a-string, or use the QR code to the right. There may also be a phone app you can install, written by the University of Colorado Boulder. You are looking for the Wave on a String simulation. In this simulation, there is a realistic string composed of a series of red and green beads. Each bead is connected to its neighbors by springs, and the laws of physics are obeyed as you shake one end. 1. [3 points] Adjust the Damping at the bottom to None. Then, in the upper-left select Pulse. In the upper-right, it should be selected on Fixed End. Now, click the green circle with a little triangle pulse icon. This should shake the left end of the string. In the space below, briefly describe what happens. (When you are done, click Restart.) 2. [3 points] Use the same settings as in question 1. However, in the upper right, now select Loose End. Again, click the green circle with a little triangle pulse icon to shake the left end. Briefly describe what happens, in particular, how it is different than what happened for question 1? (When you are done, click Restart.) 3. [3 points] Use the same settings as in question 1. However, in the upper right, now select No End. Click the green circle to shake the left end. Briefly describe what happens, in particular, how it is different than what happened for question 1? (When you are done, click Restart.)

4. Use the same settings as in question 3, with No End. However, now, in the upper-left, select Oscillate. This should set the left end wiggling up and down in Simple Harmonic Motion. (a) [2 points] Briefly describe what happens. (b) [1 point] Does the shape of the sine-wave pattern change with time? (c) [1 point] Which way does the pattern move? (d) [1 point] Which way do the individual red and green beads move? 5. [2 points] Use the same settings as question 4, with the sine-wave going out the window, Damping = None, No End, and Oscillate. However, now, near the bottom, select an Amplitude of 0.10 cm, and a Frequency of 0.42 Hz. The will be a very low-amplitude sine wave going out the window. Next, click on Fixed End. Wait a while. Briefly describe what happens below. What kind of wave do you think this is? (When you are done, click Restart.) 6. [2 points] Use the same settings as question 5, but this time select a frequency of 0.84 Hz. Click Restart and wait a while. Briefly describe what happens below. 7. [2 points] Use the same settings as question 5. Can you find a frequency for which all the green beads are nodes (sixth harmonic)? What is this frequency?