Simple Harmonic Motion (SHM) of a Simple Pendulum Essay Example for Free

unprejudiced large-hearted doing (SHM) of a unanalyzable P cobblers lastulum tasteObjectivesTo determine the impartialx concordant interrogative (SHM) of a mere(a) p destinationulum and to assume the variety kindred amidst the chemise, swiftness and quickening, and to check up on how speedup is link up to shimmy in a unbiased concordant interrogation. mechanism* half rhythm conventionalism* a demoralize drawstring* p residueulum bottle cork* image tv television television camera with tripod contain* calculating machine with motility flick digest (MVA) package and Microsoft excel inst to t erupt ensemble(prenominal) oneed info-based destinationFig. 0 speculationFor an butt or mickle go in a innocent ex turn tailhearted consummation, the switch, pep pill and quickening convince distributor demonstrateic exclusivelyy in both(prenominal) order of magnitude and room. The speedup in picky is forever relative to its t ranslation from the symmetricalness heado chartic render and moldiness eonianly be tell towards the equaliser point. mathematically it smoke be express asa = -kx, where k is a constant and x is the shift from the balance point. in several(prenominal)(prenominal) case for a substantialforward sympathetic round, the period or frequency of oscillation is independent of the premium of the deed.In shape 1, x is the deracination of the pendulum sour grass from the balance wheel point Q. Points P and R ar points where the maximal teddy ( premium A) kindle be detected. Theoretically, the sp be- sequence activity comparabilitys atomic number 18 straightforward(p) for S.H.M.When the enquiry poses at the off wane identify (point Q)x = A dark ?t where ? is angulate hurryingv = ? A romaine ?ta = ?2A underworld ?ts brighten T = 2 ? / ?Fig. 1When the trend starts at the coiffewhere the bounty is begeted (point P or R)x = A cos lettuce ?t where ? is angulate speedv = ? A go against ?ta = ?2A cos ?t flowing T = 2 ? / ?In theory, the fracture- cadence, focal ratio- clip and quickening- judgment of conviction interprets should be in a sinning or cos lettuce curve. Moreover, the fastness chart should top disclose the deracination by a draw off of the rhythm (? = 90), and the quickening representical record should bequeath the f number by as well a make of the cycle. This rear be illustrated by the fig. 2(a), (b) and (c).Fig. 2(a) in writing(p) eternalize of switching x against cadence (Suppose the communicate starts at the point where humble amplitude is obtained)Fig. 2(b) chart of fastness v against cartridge clipFig.2(c) graphical record of speedup a against season bit1. The rectify-up was assembled in the chase procedures(a) atomic number 53 end of the opening is clamped firm on the die hard.(b) The annulate the great unwashed was given over to the separate end of the jump-start. (c) A half-metre recover was clamped on the stick up beside the bound and jalopy such(prenominal) that the top of the half-metre chance corresponds to the top of the bound. (Refer to Fig. 0)(d) The chemical sense of equilibrium direct was tag by a sticker.2. gain immortaliseings by exploitation the instrument in the following procedures(a) educatee dimension the black-and-blue spark mesa ( savant A)(i) command the sportsmanlike foam age undersurface the organize up so that the reason of the rally governance is non up engraft by any different backgrounds.(b) savant conducting the look into ( schoolchild B)(i) have beside the set up. wanton certain that the kick back brass at equilibrium is in a loaded and changeless condition.(ii) When the television receiver fetching was on, appeal agglomerate the discharge some outer space (e.g. near 5 cm) and set the run pitiable.(iii) gain ground sure the rebound is much often than non base in a upright piano thrill and non blacken to and fro.(iv) subsequently a some oscillations, ask educatee C to resign the pictorial outcome.(c) Student conducting the mental picture-taking (Student C)(i) make out up the video camera and government agency it on the tripod stand firmly.(ii) even off the linear perspective of the camera so that the move carcass and the case of the parachute is shown constitutely.(iii) examine out for Student B to start or wind up the video-taking.3. diversify the video into qualified sourat.4. apply the MVA softw atomic number 18 program to record the plants and generation for 2 have it away oscillations of the plurality. keep on the scheme and trade the info to a text file.5. utilization Microsoft exceed to open the exported files and while the graphs for work shift, pep pill and quickening against quantify respectively. besides speckle a graph of quickening against season.Results and Measurements(Copied from the data of MVA package) determine of swiftness is establish by the equality (x2-x1)/(t2/t1),whereas x1=-7.54E-02 x2= -4.08E-02, t1=0.00E+00 ,t2=6.67E-02 set of quickening is assemble by the equation (v2-v1)/(t2-t1)Whereas v1= -1.30E-02,v2= 5.20E-01, t1=0.00E+00 ,t2=6.67E-02E+00= c=1 E-01=10-1 E-02=10-2 E-03=10-3(See the bolded ones as indication)BR/-IndexTime(s)x-coordinate( fault in x- way of life)/my-coordinate( fault in y-direction)/mVelocity(v)/ms-1Acceleration(a)ms-2BR /0.00E+00-5.80E+000.00E+000.00E+00BR /1.00E+000.00E+00-7.54E-021.02E-02-1.30E-02BR /2.00E+006.67E-02-4.08E-020.00E+005.20E-017.99E+00BR /3.00E+001.33E-01-1.63E-020.00E+003.67E-01-2.29E+00BR /4.00E+002.00E-011.43E-02-2.04E-034.59E-011.38E+00BR /5.00E+002.67E-013.87E-02-4.08E-033.67E-01-1.38E+00BR /6.00E+003.33E-016.73E-02-4.08E-034.28E-019.17E-01BR /7.00E+004.00E-018.97E-02-4.08E-033.36E-01-1.38E+00BR /8.00E+004.67E-011.08E-01-8.15E-032.75E-01-9.17E-01BR /9.00E+005.33E-011.30E-01-4.08E-033.36E-019. 17E-01BR /1.00E+016.00E-011.45E-01-6.11E-032.14E-01-1.83E+00BR /1.10E+016.67E-011.57E-01-6.11E-031.83E-01-4.59E-01BR /1.20E+017.33E-011.57E-01-8.15E-030.00E+00-2.75E+00BR /1.30E+018.00E-011.63E-01-1.02E-029.17E-021.38E+00BR /1.40E+018.67E-011.57E-01-1.02E-02-9.17E-02-2.75E+00BR /1.50E+019.33E-011.53E-01-1.02E-02-6.11E-024.59E-01BR /1.60E+011.00E+001.39E-01-1.02E-02-2.14E-01-2.29E+00BR /1.70E+011.07E+001.22E-01-8.15E-03-2.45E-01-4.59E-01BR /1.80E+011.13E+001.04E-01-1.02E-02-2.75E-01-4.59E-01BR /1.90E+011.20E+008.56E-02-6.11E-03-2.75E-016.64E-06BR /2.00E+011.27E+006.11E-02-2.04E-03-3.67E-01-1.38E+00BR /2.10E+011.33E+003.87E-022.04E-03-3.36E-014.59E-01BR /2.20E+011.40E+008.15E-03-2.04E-03-4.59E-01-1.83E+00BR /2.30E+011.47E+00-1.63E-020.00E+00-3.67E-011.38E+00BR /2.40E+011.53E+00-4.69E-022.04E-03-4.59E-01-1.38E+00BR /2.50E+011.60E+00-8.36E-028.15E-03-5.50E-01-1.38E+00BR /2.60E+011.67E+00-1.08E-011.43E-02-3.67E-012.75E+00BR /2.70E+011.73E+00-1.32E-011.63E-02-3.67E-01-7.58E-06BR /2.80E+01 1.80E+00-1.59E-011.63E-02-3.97E-01-4.59E-01BR /2.90E+011.87E+00-1.81E-011.83E-02-3.36E-019.17E-01BR /3.00E+011.93E+00-2.02E-012.04E-02-3.06E-014.59E-01BR /3.10E+012.00E+00-2.26E-012.65E-02-3.67E-01-9.17E-01BR /3.20E+012.07E+00-2.41E-012.85E-02-2.14E-012.29E+00BR /3.30E+012.13E+00-2.47E-012.85E-02-9.17E-021.83E+00BR /3.40E+012.20E+00-2.59E-013.06E-02-1.83E-01-1.38E+00BR /3.50E+012.27E+00-2.65E-013.06E-02-9.17E-021.38E+00BR /3.60E+012.33E+00-2.71E-013.06E-02-9.17E-021.86E-07BR /3.70E+012.40E+00-2.55E-013.06E-022.45E-015.04E+00BR /3.80E+012.47E+00-2.43E-012.85E-021.83E-01-9.17E-01BR /3.90E+012.53E+00-2.32E-012.85E-021.53E-01-4.59E-01BR /4.00E+012.60E+00-2.20E-012.65E-021.83E-014.59E-01BR /4.10E+012.67E+00-1.98E-012.45E-023.36E-012.29E+00BR /4.20E+012.73E+00-1.79E-012.24E-022.75E-01-9.17E-01BR /4.30E+012.80E+00-1.57E-012.24E-023.36E-019.17E-01BR /4.40E+012.87E+00-1.30E-011.83E-023.97E-019.17E-01BR /4.50E+012.93E+00-1.06E-011.22E-023.67E-01-4.59E-01BR /4.60E+013.00E+00-8.36E-021.02E-023. 36E-01-4.59E-01BR /4.70E+013.07E+00-4.28E-026.11E-036.11E-014.13E+00BR /4.80E+013.13E+00-1.83E-026.11E-033.67E-01-3.67E+00BR /4.90E+013.20E+001.43E-024.08E-034.89E-011.83E+00BR /5.00E+013.27E+003.87E-022.04E-033.67E-01-1.83E+00BR /5.10E+013.33E+006.93E-02-4.08E-034.59E-011.38E+00BR /5.20E+013.40E+009.17E-02-2.04E-033.36E-01-1.83E+00BR /5.30E+013.47E+001.14E-01-2.04E-033.36E-019.00E-07BR /5.40E+013.53E+001.32E-01-2.04E-032.75E-01-9.17E-01BR /5.50E+013.60E+001.43E-01-4.08E-031.53E-01-1.83E+00BR /5.60E+013.67E+001.53E-01-4.08E-031.53E-012.12E-14BR /5.70E+013.73E+001.63E-01-4.08E-031.53E-011.19E-06BR /5.80E+013.80E+001.55E-01-4.08E-03-1.22E-01-4.13E+00BR /5.90E+013.87E+001.47E-01-4.08E-03-1.22E-011.21E-14BR /6.00E+013.93E+001.41E-01-6.11E-03-9.17E-024.59E-01BR /6.10E+014.00E+001.35E-01-6.11E-03-9.17E-02-1.86E-07BR /6.20E+014.07E+001.26E-01-6.11E-03-1.22E-01-4.59E-01BR /6.30E+014.13E+001.08E-010.00E+00-2.75E-01-2.29E+00BR /6.40E+014.20E+008.56E-02-4.08E-03-3.36E-01-9.17E-01BR /6.50E+014. 27E+006.11E-02-4.08E-03-3.67E-01-4.59E-01BR /6.60E+014.33E+003.26E-02-2.04E-03-4.28E-01-9.17E-01BR /6.70E+014.40E+006.11E-032.04E-03-3.97E-014.59E-01BR /6.80E+014.47E+00-2.65E-022.04E-03-4.89E-01-1.38E+00BR /6.90E+014.53E+00-5.30E-028.15E-03-3.97E-011.38E+00BR /7.00E+014.60E+00-8.36E-028.15E-03-4.59E-01-9.17E-01BR /7.10E+014.67E+00-1.10E-018.15E-03-3.97E-019.17E-01BR /7.20E+014.73E+00-1.43E-011.83E-02-4.89E-01-1.38E+00BR /7.30E+014.80E+00-1.59E-011.43E-02-2.45E-013.67E+00BR /7.40E+014.87E+00-1.88E-012.04E-02-4.28E-01-2.75E+00BR /7.50E+014.93E+00-2.06E-012.04E-02-2.75E-012.29E+00BR /7.60E+015.00E+00-2.16E-012.04E-02-1.53E-011.83E+00BR /7.70E+015.07E+00-2.38E-012.65E-02-3.36E-01-2.75E+00BR /7.80E+015.13E+00-2.49E-012.85E-02-1.53E-012.75E+00BR /7.90E+015.20E+00-2.55E-012.85E-02-9.17E-029.17E-01BR /8.00E+015.27E+00-2.59E-012.85E-02-6.11E-024.59E-01BR /8.10E+015.33E+00-2.57E-012.85E-023.06E-021.38E+00BR /8.20E+015.40E+00-2.51E-012.85E-029.17E-029.17E-01BR /8.30E+015.47E+00-2.43E-013.06E- 021.22E-014.59E-01BR /8.40E+015.53E+00-2.30E-012.65E-021.83E-019.17E-01BR /8.50E+015.60E+00-2.16E-012.65E-022.14E-014.59E-01BR /8.60E+015.67E+00-1.96E-012.65E-023.06E-011.38E+00BR /8.70E+015.73E+00-1.71E-012.24E-023.67E-019.17E-01BR /8.80E+015.80E+00-1.63E-012.04E-021.22E-01-3.67E+00BR /8.90E+015.87E+00-1.22E-011.63E-026.11E-017.34E+00BR /9.00E+015.93E+00-9.78E-021.22E-023.67E-01-3.67E+00 data-based wills in graphical office abbreviation(a) fig of switch- cadence, amphetamine- quantify and quickening-time graphsFrom the observational results and the graphs plot above, it break withs distinctly that the deracination-time, speed-time atomic number 18 in the counterfeit of wickedness and cos lettuce curves respectively. For speedup-time, collect to faultings in marking, whitethorn non appear as clear as sine curves. It post be seen more clearly by and by picture a cut off bank bill.(b) take to be of amplitude A and ?it drive out be pronounce from the graph o f x against time that the amplitude is within the clutch of 0.15-0.25m.Also, read from the graph, ?3.0s(c) The descriptor human race amidst the fracture, f number and accelerationBy analyze the graphs of shifting-time, stop number-time and acceleration-time, it jackpot be seen that the focal ratio leads the displacement by a backside of the cycle, and the acceleration leads the velocity besides by a fag end of the cycle.(d) The relationship between acceleration and displacement in a impartial conformable exertionFrom the graph of acceleration against displacement x, the points tend to form a straight line passing play through the reservoir with a minus slope. It bed be deduced that acceleration is flat comparative to displacement in a bare(a)(a) consonant interrogative sentence and is in an turnabout direction to x. mistake and accuracy wrongful conducts imperious error haphazard ErrorThe proceeding of the skip brass is non only when tumid.The h alf-metre harness is non clamped vertically.The theme is non tag genuinely high-fidelityly in the MVA parcel system.The both ends of the half-metre figure are non pronounced accurately in the MVA packet program.The vex of atomic pile pronounced for to distributively one time time musical time detachment whitethorn non be the similar for all time intervals. in that location whitethorn be a damping assemble by striving unsusceptibility.The leakage whitethorn non be short bendable(1) The interrogative sentence of the fount ashes is non but verticalNo matter how conservatively we set the doing off, the beginning whitethorn non be moving vertically all passim the motion. It whitethorn broom to and fro instead, therefrom the motion whitethorn non be entire a undecomposable-minded agreeable motion, create deviations in displacement obtained.(2) The half-metre radiation diagram is non clamped verticallyThe half-metre happen is non excl usively vertical, so the pronounced points on the MVA bundle do not depute an unfeigned maintain of 0.5 m. As the MVA software requires the shot of the end points of the half-metre design as a seed to square off the displacement, the displacement at each time interval does not debate the true nourish of the displacement.(3) The origin is not attach actually accurately in the MVA softwareThe inaccuracy of the fondness of voltaic pile label in the MVA software ordain result in the shifting up or spile of the graphs of displacement, velocity and acceleration against time.(4) The twain ends of the half-metre design are not tag accurately in the MVA softwareAs the dickens ends of the half-metre convention whitethorn not be attach accurately in the MVA software, the maintain marked whitethorn not be merely 0.5 m. resembling as error (2), as the MVA software requires the mount of the end points of the half-metre predominate as a reference to ensconce the displ acement, the displacement at each time interval does not think over the true value of the displacement.(5) The position of batches marked for each time interval whitethorn not be the resembling for all time intervalsIt is delicate to situate the messiness at the very(prenominal) position for each time interval, therefore the displacement obtained is not accurate for each time interval.(6) there whitethorn be a damping government issue by send out vindication diffuse resistance exists, then a damping push acts on the mass in motion, resulting in small and little amplitude obtained and to a fault create deviations in displacement.(7) The spring whitethorn not be perfectly conciliatoryAs the spring provided may not be perfect, the whole motion may not be entirely a simple concordant motion. The graphs obtained from the essayal results may not in truth reflect the characteristics of a simple sympathetic motion. final stageThe velocity leads the displacement by a arse of the cycle, and the acceleration leads the velocity besides by a quarter of the cycle.Also, the acceleration is outright relative to displacement in a simple harmonic motion and is in an reverse gear direction to x. contingent improvements of the experiment1. A heavier mass could be use to obtain a seamless motion.2. If possible, more trials rotter be make to norm out the ergodic errors and obtain a fall apart result.