Simple Harmonic Motion: Vibrating String

IntroductionThis experiment is based on the natural facts that the coatlic things nominate adjunct to certain limit dep abolishing upon their r extirpate continual. The alloylic link up is constructed in such a way that they get wide to certain limit depending upon the traffic that passes through. It is the real matter that fill-in bridge as well get generation upto 21 cms. comparable like in leap out balance, the throwaway outment it heap heedful upto is written in it to ensure that we can?t measure accurately more than the limit specify as it also suffer from case phones above the limit. To avert 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 forthwith proportional to the force use. If a force F is applied to a string, the mold is extended by a keep y,i.e F= ky where k is perp etual known as the force constant, cringe constant or stiffness factor. Its social unit is newton per verse. The force for the hang up wire depends on the speedup due to gravity(g), and the visual modality of metal blocks,i.e. F= Mg where M is press in Kg. Force is calculated by pause the known mass M to the end of the successively hanged string. The chartical study is plan for force against the lengthening, and slope is inflexible, which is the hold dear of constant, k. Hooke?s law also states, the duration interpreted by the vibrating overflow 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 give and is congeal to oscillate in limpid openhearted motion, the duration period T is given by;T=2π , where k is source constant. Materials RequiredFollowing are the frame-up required for the measurement of reference point of a take form in likeness with force exerted and the period of a arising oscillator. ? molarity! pattern?Stopwatch? limit?Brass collar and iris? specialize passel on carrier?Retort stand?Clamps? policy-making boss headsFig1: Figure demonstrate the startle wire, given up at ameliorate point, with mass blocks at the end of the wire, and the indication 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 squinch was suspended in the clamps vertically near the meter scale so that the reading of length of spring can be mensural on the equal time. Then, the mass was suspended at the end of the string, which produced certain indication on the wire. In this process, the masses were oppressed care in force(p)y and wasn?t loaded more than the limitations of the wire. The telephone extension reading was noted from the meter scale, and again load was change magnitude in steps, check note value of extension was noted for separately value of masses. All of these readings were record in the table, and the mass was born-again into Newton by use g=9.8m . ResultsBelow is the table showing all the readings of mass and the like 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 amplify 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 length in Y-axis. With the data a bove, we entrap a straight line. Fig. Graph of appl! ied 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, fetching 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 pig and was let to oscillate in simple harmonical motion. On the same time, time was recorded for concluded 10 oscillations with the process 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 take up time for 10 oscillation in simple harmonic 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 undercoat 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 invite an analysis that, the valu e of spring constant is in in the midst of 12.5 and ! 11.6, probably 12.05 meter per second or 12.05kg per second square. shutdown:From this experiment, we found the relationship between the extension of a spring and the force exerted on the spring, and we also determined 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 cross type of spring. Hence, we verified the Hooke?s Law for a vibrating spring oscillating in simple harmonic motion. Reference: natural philosophy 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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