Lab report no 2 pemdulum phyisc 212
- 1. CALIFORNIA STATE UNIVERSITY, LOS ANGELES Department of Physics and Astronomy Physics 212-14 / Section 14- 34514 Standing waves On Strings Prepared by: Faustino Corona, Noe Rodriguez, Rodney Pujada, Richard Lam Performance Date: Tuesday,April 6, 2016 Submission Due: Tuesday, April 13, 2016 Professor: Ryan Andersen Wednesday: 6:00 pm. – 8:30 p.m. April 2016
- 2. Experiment No 2: Pendulums I. ABSTRACT To experiment the relation between wave velocity and spring’s tension by using standing waves II. INTRODUCTION In this experiement we are using an electrically driven vibrartor of 60HZ frequency that is attached to a set of weights with a weight holder. f=frequency in cycles/second (HZ) λ=wavelength v=f λ, the speed of propagation of the wave in any medium τ =tension in the string, equal to "mg" if produced by a hanging mass "m" μ =mass per unit length of the string VTH=, the theoretical speed of propagation of a wave along a string under tension k=2π/λ, the wavenumber of the wave ω =2f=kv III. EXPERIMENTAL PROCEDURE
- 3. IV. DATA AND ANALYSIS 4.1. SINGLE PENDULUM : DEPENDENCE OF PERIOD ON LENGTH DATA TABLE 1: For this part of the experiment the mass was fixed at 50 g. L(cm) L(m) T (seconds) No Cycles Period (T) T 2 (s) 10 0.1 5.43 10 0.543 0.295 20 0.2 8.56 10 0.856 0.733 40 0.4 12.26 10 1.226 1.503 80 0.8 18.03 10 1.803 3.251 120 1.2 22.49 10 2.249 5.058 160 1.6 25.82 10 2.582 6.667 DATA TABLE 2: All times are measure in seconds. L(m) T 2 (s) 0.1 0.295 0.2 0.733 0.4 1.503 0.8 3.251 1.2 5.058 1.6 6.667 GRAPH PERIOD (T2 )VS LENGTH : The data was copied into Excel and graphed, showing the linear regression. Graph No 1 : Period Vs Length for simple pendulum
- 4. The linear equation is T2 = 4.2799L - 0.1494 with a correlation of R² = 0.9997 We have our equation T2 = (4π2 / g) L where (4π2 / g) is the slope in our graph. 4.2. PHYSICAL PENDULUM: PERIOD VS ANGLE DATA TABLE 4 T/2 (seconds) (°)ϴ Period (T) 4.65 30 9.3 4.87 60 9.74 4.99 90 9.98 5.5 120 11 6.81 150 13.62 8.66 180 17.32 Graph No 2 Period vs angle.
- 6. a) Measure the period for normal mode #1 OBSERVATIONS: Both masses have the same frequency and direction when they are release. Every pendulum has a natural or resonant frequency, which is the number of times it swings back and forth per second. The resonant frequency depends on the pendulum’s length. Longer pendulums have lower frequencies. b) Measure the period for normal mode #2 OBSERVATIONS: In opposite directions both masses have the same frequency. c) Measure the period for normal mode # 3 OBSERVATIONS: Observe this “energy exchange motion”. Note that the total amount of energy in the system remains constant, but it is constantly being passed between the two pendula. Pendulum 2 speeds up at the expense of pendulum 1 slowing down, and vice versa. The energy “sloshes” back and forth between the two parts of the system. The spring provides the transfer mechanism. This simple system models the complex energy transfers that occur in nature. We observe measure the period of energy exchange. DATA TABLE 5: Couple Pendulums : Experiment changing the mode. Coupled Pendulums T(seconds) L (cm) Height of connection between pendulum Mode # 1 14.83 32.5 Mode # 1 14.8 13.5 Mode # 2 9.8 32.5 Mode # 2 13.16 13.5
- 7. Mode # 3 3.04 32.5 Mode # 3 11.65 13.5 4.4. CALCULATION OF G Where the slope is 4.2799. Therefore 4.2799 = 4 π2 / g Find g: 4.2799 The graph No 1 show the dependence of T2 on L, where the slope of the graph is Since slope = 4.2799 g = (2π) 2/slope = (2π) 2 / 4.2799 g = 9.22m/s2 g = 9.22m/s2 The error here, comparede to the expected value of g = 9.80 m/s2 is 4.5 CALCULATION OF PERCENT DIFFERENCE We appreciate Calculate the percent of error: Percent error = ( Dpractical — Dtheoric) x 100 % … formula 1 Average(practical value + Theorycal value)/2 Data: g= 9.22 m/s2 ( graph No 1 (calculation from slope in the graph part 4.4) g = 9.8 m/s2 to evaluate percent of error. Average(practical value + Theorycal value)/2 = (9.22+ 9.80 )/2 = 9.51 Percent error = {(9.22 - 9.88) / 9.51 }x100% = -6.1 % 9.51 Percent error = -6.1 % V. RESULTS This experiment has three parts: For simple pendulum, they do not dependence from angle and mass. We calculate by the linear regression the slope of 4.2799. We can calculate a practical value 9.22 m/s2 The period vs. length measurements were well described by a power law. Using Excel to fit the data, the best power-law fit is: From the second part: We appreciate the physical pendulum do not depende form the angle ( graph No 2)
- 8. From the last part: A small error is introduced by assuming that the motion is simple harmonic. (A real pendulum only approximates simple harmonic motion.) There is some friction in the string where it moves on the metal rod, and there is some air friction. Also, the theoretical value used for g may be slightly off due to local variations in its value. There may be some error introduced by imperfections in the ruler used to measure length and in the stopwatch. An additional error is introduced by the innate variation in human reaction time when operating the stopwatch. VI. CONCLUSIONS From the results of our experiment we can observe that in the insistence of Period (Time) vs. Length we notice that if you stretch it 10 cm or 180 cm the Period would increase as the length increases. This dependence how much time between the Periods (T) since timing is a big factor when doing this experiment and some slight error might occur in timing. But when you observe the experiment, when length is no longer in account but amplitude is you would notice the change in time would not change if surface is frictionless. If more of an angle is add the time should be similar and reach the ten cycles we are using to observe at the same time in this experiment. Some agreements with the predictions is that the amplitude should not have an effect on period because at first there were close in time but then we notice that friction in the disk was causing it to slow down and that length does have an effect on period depending on the amount of length placed on the spring. I have to disagree with some results since without precision some numbers would be off. For example period because timing is an issue since we can never get the time right this is why we had to do ten cycles to get the most precision in this experiment. Another issue was measurements because we did not have a precise measurement technique we had to eyeball the lengths of the strings and also if it’s close to the amplitudes we want. Meaning that in some instances the amplitude we want to reach can be a bit over or under meaning that this can make the error a bit more than it should. Some possible improvements are finding new ways to measure distances more accurately and time as well. VII. REFERENCES • Department of Physics and Astronomy CSU Los Angeles. Edition 2.0, XanEdu Custom Publishing, pp. 8-14 VIII. DATA SHEETS