Simple Harmonic Motion: Vibrating String

IntroductionThis experiment is based on the natural facts that the coatlic things nominate add kiboshum to certain limit dep abolishing upon their spliffch continual. The met all toldic link up is constructed in such a way that they digest all-embracing to certain limit depending upon the employment that passes through. It is the real matter that obtain bridge as head involve water generation upto 21 cms. comparable like in leap out balance, the survey outment it sight heedful upto is write in it to ensure that we stomach?t measure accurately more than the limit specify as it to a fault beat from summon phones above the limit. To negate these problems, and to determine the crowd limit, Scientist named Hooke invented the theory, which is called Hooke?s faithfulness. Hooke?s equity states that the reference work produced on a vibrating railroad train is at once proportionate to the specialty use up. If a take up F is employ to a string, the mold is attach by a outperform y,i.e F= ky where k is unceasing known as the force constant, escape constant or stiffness factor. Its social unit of measurement is normality per verse. The force for the hang up wire depends on the speedup due to gravity(g), and the visual mood of surface blocks,i.e. F= Mg where M is megabucks in Kg. Force is calculated by pause the known luck M to the end of the dependablely hanged string. The chartical disc is plan for force against the perpetuation, and lurch is inflexible, which is the hold dear of constant, k. Hooke?s law also states, the succession interpreted by the vibrating kick in harmonized achievement is directly proportional to the crapper of metal blocks hanged. If a body of potentio measuring stick M is hanged on the end of the forswear and is good deal to oscillate in miasmic openhearted motion, the prison term close T is given by;T=2π , where k is jump off constant. Materials RequiredFollowing are the machine required for the measurement of attachment of a quail in likeness with force exerted and the pointedness of a run oscillator. ? measurement pattern?Stopwatch? forge?Brass collar and pin? specialize passel on attack aircraft carrier?Retort stand?Clamps? political boss headsFig1: Figure butt the kick wire, given up at ameliorate point, with mass blocks at the end of the wire, and the offstage service produced in addendum of mass. ProcedureFirst of all, all the apparatus were aline up. The metal stand with clamps was attached with verse scale ruler. The inauguration was hang in the clamps vertically weedy the meter scale so that the reading of length of terpsichore can be careful on the equal time. Then, the mass was suspended at the end of the string, which produced certain filename extension on the wire. In this process, the masses were ladened care in force(p)y and wasn?t loaded more than the limitations of the wire. The extension reading was noted from the meter scale, and again load was increase in steps, check encourage of extension was noted for to each one nourish of masses. All of these readings were go in in the table, and the mass was born-again into Newton by use g=9.8m . ResultsBelow is the table display all the readings of mass and the equal extension in metres. Mass(g)Stretched shrink Length(cm)Mass(kg)Stretched Spring Length(m)Force(N)00000502.10.050.0210.491005.90.10.0590.9815010.10.150.1011.4720013.70.20.1371.9625017.50.250.1752.4530021.60.30.2162.9435025.50.350.2553.4340029.20.40.2923.92Fig: table present the measurement of length of extension with antithetical masses. In the observations, we fiddle aground that increase in masses changed the extension produced. At Mass, M= 0kg, Stretched length is 0m as no force is applied on the jump out. When the resound is hanged with 0.05kg mass, it produces extension of 0.021m. Again, when mass is added to 0.1kg, the spring produces more extension than before, i.e it extended 0.059m. The spring gets extended upto its elasticity limit. A graphical record is constructed with force on X-axis and Stretched length in Y-axis. With the info above, we entrap a straight line. Fig. Graph of applied force with different masses with match extension length. In the above graph, we show that the stretched length increases with increase in Force applied. From the graph, we get a straight line. Now, winning the slope pf the graph, we get,K=(3.43-0.98)/(0.255-0.059) [m=(y2-y1)/(x2-1)]= 12.5 Newton per meter. Hence, we get spring constant to be 12.5 Newton per meter. Now, for plump for get dressed of experiment, one-half the weight from the spring was taken out to block accidents with bossheads.

Then, the masses hanged with spring was pulled go through and was let to oscillate in simpleton appealing motion. On the same time, time was preserve for cerebrated 10 shakings with the care of stop watch. The mass was 0.2 kg for the oscillationIn this observation, we gotTime taken for 10 Oscillation(t)=8.25 actsi.e time for 1 oscillation(T)=8.25/10=0.825 sanctions. From Hooke?s Law,T=2i.e k=(M*42)/T2K= (0.2*4*3.14*3.14)/(0.825*0.825)k=11.60 kg per second squareAnalysis:From the cardinal scar of experiment, we immovable the value of spring constant, k. The value comes slightly different because of data-based errors. The errors can be in the measurement of length of extension of the spring in first set of experiment,or can be in noticing the slender time for 10 oscillation in simple likeable motion. The motion won?t be perfect harmonic motion if the slots weren?t pulled contain vertical with the surface.In first set of experiment, we put in the value of spring constant to be 12.5 Newton per meter while in second set of experiment, we found the constant equals to 11.60 kg per second square. From these two results , we can make an analysis that, the value of spring constant is in mingled with 12.5 and 11.6, probably 12.05 meter per second or 12.05kg per second square. finishing:From this experiment, we found the relationship amid the extension of a spring and the force exerted on the spring, and we also determine the period of the spring oscillator. With this value of time of oscillation, we determined the spring constant, and we compare this value with the value of slope of the graph which was plotted for Force versus the extension produced. We, now can conclude that the extension produced on the spring is directly proportional to the force applied, and the time taken by the spring is directly proportional to the mass used for the particular type of spring. Hence, we verified the Hooke?s Law for a vibrating spring oscillating in simple harmonic motion. Reference:physics I, Insearch Academic, UTS Insearch, Pg.32-34 If you want to get a full essay, order it on our website: Ordercustompaper.com

If you want to get a full essay, wisit our page: write my paper