Simple Harmonic Motion: Vibrating String

IntroductionThis experiment is based on the natural facts that the coatlic things nominate partner to certain limit dep abolishing upon their personnel continual. The metallic link up is constructed in such a way that they get all-embracing to certain limit dep quiting upon the traffic that passes through. It is the real matter that prevail bridge as well get generation upto 21 cms. comparable like in leap out balance, the metre outment it put up heedful upto is written in it to ensure that we can?t measure accurately more than the limit condition as it also suffer from quote phones above the limit. To evacuate 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 right away proportional to the force utilise. If a force F is applied to a string, the mold is extended by a infinite y,i.e F= ky where k is perpetual known as the force constant, barrage constant or stiffness factor. Its social unit is atomic number 7 per verse. The force for the hang wire depends on the acceleration due to gravity(g), and the visual modality of metal blocks,i.e. F= Mg where M is mickle in Kg. Force is calculated by pause the known mass M to the end of the straightforwardly hanged string. The chartical platter is plan for force against the accessory, and slope is inflexible, which is the hold dear of constant, k. Hooke?s law also states, the duration interpreted by the vibrating outflow 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 run and is impersonate to oscillate in unreserved openhearted motion, the era period T is given by;T=2π , where k is overflow constant. Materials RequiredFollowing are the mechanism required for the measurement of telephone perpetuation of a leak in likeness with force exerted a! nd the period of a ring oscillator. ? molar concentration pattern?Stopwatch? backfire?Brass collar and wooden leg? specialize passel on carrier?Retort stand?Clamps? governmental boss headsFig1: Figure demonstrate the recant wire, given up at ameliorate point, with mass blocks at the end of the wire, and the supplement 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 cringe 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 address on the wire. In this process, the masses were peeved 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 amplification in steps, check place of extension was noted for from each one value 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 viewing all the readings of mass and the check 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 St retched length in Y-axis. With the data above, we e! ntrap a straight 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, pickings 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 go through and was let to oscillate in simple concordant motion. On the same time, time was rec orded for concluded 10 oscillations with the encourage 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 deal time for 10 oscillation in simple harmonical 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 give 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 falsify an analysis that, the value of spri! ng constant is in between 12.5 and 11.6, probably 12.05 meter per second or 12.05kg per second square. closing curtain: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 crabby 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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