M-12b: SHM and Resonance Name_______________________ Lab Worksheet Group member names__________________________________ 1 This work sheet is the lab document your TA will use to score your lab. It is to be turned in at the end of lab. M-12b Simple Harmonic Motion and Resonance: The lab has many parts but you will do only the following four. Experiment I demonstrates that the period is independent of the amplitude. Experiment II demonstrates that the period varies with mass. Experiment III is about finding k with Hooke’s Law. Experiment VI is about forced oscillations and resonance. Experiment I: Once you are comfortable with the operation of the glider on the air track then measure the period, T, at three in different amplitudes. Suggested amplitudes of approximately 10 cm, 20 cm, and 30 cm. (Friction may be a problem at very small amplitudes). Do you expect the amplitudes to be the same or different (why or why not)? Brief Description of Actual Experimental Procedure: Amplitude (A ±∆A) Period Trial 1(T±∆T) Period Trial 2(T±∆T) NotesM-12b: SHM and Resonance Name_______________________ Lab Worksheet 2 Do your results indicate that the period varies with amplitude? Experiment II: In this experiment you will measure the period as a functions of cart mass. Measure the mass of the cart and that of the springs. Now average your results of Experiment I and fill in the table entries making sure to use SI units (kg, m, s). Mass Spring 1 Mass Spring 2 Mass Cart Effective Mass Meff Average Period Spring Constant k’ m1 m2 MC MC + (m1+m2)/3 TAvg. 4π2 Meff / Tavg2 And mass to the carts and repeat the experiment using enough trials to achieve similar results. Mass added:_______________ What is your expected period?____________ Show work below: Now measure the new period and fill in the table on the next page. Amplitude (A ±∆A) Period (T±∆T) Notes Mass Spring 1 Mass Spring 2 Mass Cart Effective Mass Meff Average Period Spring Constant k’’ m1 m2 MC MC + (m1+m2)/3 TAvg. 4π2 Meff / Tavg2M-12b: SHM and Resonance Name_______________________ Lab Worksheet 3 Are your results consistent with your expected period with the additional mass? Experiment III: Your TA will show you the “knife edge” used to measure the spring constant, k. Record data, plots and calculations below. Include brief explanations so a reader can follow your calculations and know where all your numbers come from. Trial Mass (kg) Weight (N) Spring 1 Displacement (m) Mass (kg) Weight (N) Spring 2 Displacement (m) 1 2 3 4 Plot Force vs. displacement and find the slopes.M-12b: SHM and Resonance Name_______________________ Lab Worksheet 4 Spring 1 slope k1 (N/m) Spring 2 slope k2 (N/m) k1 + k2 k’ k’’ Are your results consistent with the spring constants you obtained from the SHM experiment? Experiment VI: (This one uses the software file from Experiment V.) Do procedures and questions from step 1-10 and record your data, plots, tables, and calculations below. Ignore references to R/m. Please use complete sentences. Explain your calculations. Play close attention to how long it takes to reach the steady state solution. Also note that the drag forces in this experiment aren’t exactly proportional to the speed.M-12b: SHM and Resonance Name_______________________ Lab Worksheet 5M-12b: SHM and Resonance Name_______________________ Lab Worksheet 6 Final Questions: (1) If the drag force were to become much smaller what do you think would happen theoretically, experimentally? (2)If the speaker were attached to an amplifier playing audible music (nominally 20-20,000 Hz), what do you think this the mass will
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