Damped Harmonic Motion Lab Report Essay Example

Damped Harmonic Motion Lab Report Essay Example Damped Harmonic Motion Lab Report Paper Damped Harmonic Motion Lab Report Paper The graphs created were transferred into Igor Pro, where a non-linear fit was created. From this fit, the damping constant of the objects motion was given, and the effect of air resistance on the object was determined. A relationship was discovered between the objects area and the effect air resistance had. The results showed that with a greater area of the object, there was more air resistance on the object. Introduction The goal of this experiment was to observe the effect that the size of an object ad on the air resistance shown when the object was in motion. In order to do this, a damping coefficient was determined through non-linear fits of position graphs produced during its motion. The damping coefficient shows the effect that the damping†air resistance†has on the object, shown by a gradual decrease in the size of the amplitude of its oscillations. The damping coefficient is represented by the variable b. Equation 1 shows the non-linear fit used to retrieve the damping coefficient. Equation 1: Where: A = Amplitude b = damping coefficient m = mass (held constant) frequency = objects initial displacement = objects equilibrium position Experimental Description For this experiment, a spring was suspended in the air, and objects of different area were placed on the end of the spring. A sonic ranger motion sensor was positioned on the ground directly below the object, and after the object was pulled and allowed to rise and fall, the motion sensor graphed the its position. Four trials were conducted, and before each trial, the object was replaced with that of a larger area. The graphs produced were transferred into Igor Pro, and hen, using Equation 1, a non-linear fit was produced, which yielded the value of the damping coefficient needed to make observations about the effect the size of an object had on air resistance. Data and Analysis For each trial, the position of the object was recorded and graphed, and then transferred into Igor Pro. In Igor Pro, a line of best fit was created. The specific radius of the object was recorded for each trial as well, in order to calculate its area. Graph 1 shows the original graph for Trial 1, shown by the black markers, long with the line of best fit produced, which is shown in red. The radius of the object in Trial 1 was 0. 07 m. Graph 1: Trial 1 initial graph with line of best fit Graph 2 shows the graphs produced in Trial 2, where an object with a radius of 0. 086 m was used. Graph 2: Trial 2 initial graph with line of best fit Graph 3 shows the graphs produced in Trial 3, where an object with a radius of 0. 1 m was used. Graph 3: Trial 3 initial graph with line of best fit Graph 4 shows the graphs produced in Trial 4, where an object with a radius of 0. 115 m was used. Graph 4: Trial 4 initial graph with line of best fit For each of the graphs shown above, a line of best fit equation was also given. In this equation, the value of b, the damping coefficient, was shown.