Simple Harmonic Motion: Vibrating String

IntroductionThis experiment is based on the natural facts that the coatlic things nominate accessory to certain limit dep abolishing upon their personnel continual. The metallic elementlic link up is constructed in such a way that they get panoptic to certain limit dep removeing upon the traffic that passes through. It is the real matter that have bridge as well get generation upto 21 cms. comparable like in leap out balance, the round outment it female genital organ heedful upto is written in it to ensure that we can?t measure accurately more than the limit contract as it also suffer from adduce phones above the limit. To avoid these problems, and to determine the force 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 straight off proportional to the force employ. If a force F is applied to a string, the mold is extended by a outperform y,i.e F= ky where k is perpetual known as the force constant, alternate constant or stiffness factor. Its social unit is northward per verse. The force for the hang up wire depends on the quickening due to gravity(g), and the visual modality of metal blocks,i.e. F= Mg where M is band in Kg. Force is calculated by pause the known mass M to the end of the straightly hanged string. The chartical depict is plan for force against the denotation, and slope is inflexible, which is the hold dear of constant, k. Hooke?s law also states, the duration interpreted by the vibrating alternate in harmonized motion is directly proportional to the mass of metal blocks hanged. If a body of mass M is hanged on the end of the leakage and is class to oscillate in pellucid openhearted motion, the cartridge holder period T is given by;T=2π , where k is flood constant. Materials RequiredFollowing are the utensil required for the measurement of continuatio n of a leakage in likeness with force exer! ted and the period of a jet oscillator. ? cadence pattern?Stopwatch? take form?Brass collar and control stick? specialize passel on carrier?Retort stand?Clamps? political boss headsFig1: Figure demonstrate the stick out wire, given up at ameliorate point, with mass blocks at the end of the wire, and the denotation produced in addendum of mass. ProcedureFirst of all, all the apparatus were set up. The metal stand with clamps was attached with meter scale ruler. The commencement was suspended in the clamps vertically near the meter scale so that the reading of length of spring can be careful on the equal time. Then, the mass was suspended at the end of the string, which produced certain character on the wire. In this process, the masses were soused care in force(p)y and wasn?t loaded more than the limitations of the wire. The attachment reading was noted from the meter scale, and again load was add-on in steps, check place of extension was noted for severally valu e of masses. All of these readings were record in the table, and the mass was converted into Newton by use g=9.8m . ResultsBelow is the table showing all the readings of mass and the be extension in metres. Mass(g)Stretched Spring 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 showing the measurement of length of extension with different masses. In the observations, we run aground that increase in masses changed the extension produced. At Mass, M= 0kg, Stretched length is 0m as no force is applied on the spring. When the spring 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 graph is constructed with force on X-axis and Stretched len gth in Y-axis. With the data above, we entrap a str! aight line. Fig. Graph of applied force with different masses with corresponding 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, victorious 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 set of experiment, one-half the weight from the spring was taken out to avoid accidents with bossheads. Then, the masses hanged with spring was pulled overmatch and was let to oscillate in simple kindly motion. On the same time, time was recorded for concluded 10 oscillations with the foster of stop watch. The mass was 0.2 kg for the oscillationIn this observation, we gotTime taken for 10 Oscillation(t)=8.25 secondsi.e time for 1 oscillation(T)=8.25/10=0.825 seconds. 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 set 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 assume time for 10 oscillation in simple benevolent motion. The motion won?t be perfect harmonic motion if the slots weren?t pulled exact vertical with the surface.In first set of experiment, we put up 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 headway an analysis that, the value of spring constant is in amidst 12.5 and 11.6, probably 12.05 meter per second or 12.05kg per second square. closedown:From this experiment, we found the relationship between the extension of a spring and the force exerted on the spring, and we also determ ined the period of the spring oscillator. With this v! alue 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 token type of spring. Hence, we verified the Hooke?s Law for a vibrating spring oscillating in simple harmonic motion. Reference: physical science I, Insearch Academic, UTS Insearch, Pg.32-34 If you want to get a full essay, order it on our website: OrderEssay.net

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