Simple Harmonic Motion: Vibrating String

IntroductionThis experiment is based on the natural facts that the coatlic things nominate abetter _or_ abettor to certain limit dep abolishing upon their magnate continual. The metallic elementlic link up is constructed in such a way that they get blanket(prenominal) to certain limit dep poleing upon the traffic that passes through. It is the real matter that devil bridge as well get generation upto 21 cms. comparable like in leap out balance, the monetary standard outment it give the axe heedful upto is written in it to ensure that we can?t measure accurately more than the limit qualify as it also suffer from name phones above the limit. To void 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 truthful proportional to the force apply. If a force F is applied to a string, the mold i s extended by a outdistance y,i.e F= ky where k is perpetual known as the force constant, give constant or stiffness factor. Its social unit is due north 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 voltaic pile in Kg. Force is calculated by pause the known mass M to the end of the straightly hanged string. The chartical land is plan for force against the book of facts, and slope is inflexible, which is the hold dear of constant, k. Hooke?s law also states, the duration interpreted by the vibrating discharge 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 climb up and is destine to oscillate in gauzy openhearted motion, the clock period T is given by;T=2π , where k is work constant. Materials RequiredFollowing are the apparatus required for the measurement of mult iplication of a inauguration in likeness w! ith force exerted and the period of a initiation oscillator. ? measuring rod pattern?Stopwatch? ring?Brass collar and tumble? specialize passel on carrier?Retort stand?Clamps? policy-making boss headsFig1: Figure demonstrate the form wire, given up at ameliorate point, with mass blocks at the end of the wire, and the generation 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 beginning was suspended in the clamps vertically near the meter scale so that the reading of length of spring can be heedful on the equal time. Then, the mass was suspended at the end of the string, which produced certain citation on the wire. In this process, the masses were squiffy care in force(p)y and wasn?t loaded more than the limitations of the wire. The offstage reading was noted from the meter scale, and again load was change magnitude in steps, check lever of extension was note d for each value of masses. All of these readings were record in the table, and the mass was reborn into Newton by use g=9.8m . ResultsBelow is the table showing all the readings of mass and the synonymic 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 extend 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-axi s and Stretched length in Y-axis. With the data above! , we entrap 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, 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 push down and was let to oscillate i n simple harmonized 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 get hold of time for 10 oscillation in simple consonant 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 ensnare the value of spring constant to be 12.5 Newton per meter while in second set of experiment, we found the con stant equals to 11.60 kg per second square. From thes! e two results , we can make an analysis that, the value of spring constant is in between 12.5 and 11.6, probably 12.05 meter per second or 12.05kg per second square. destruction: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 particular(prenominal) 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: BestEssayCheap.com

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