# 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 tooth object’s motion was given, and the effect to air resistance on the object was determined. A relationship was discovered between the objects area and the detect 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 venue 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 = object’s 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 Off 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, oeuvre 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. Mm 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.

In order to determine the effect that the size of an object had on the air resistance, a graph was created, comparing the area of the object with its corresponding value of b. Table I shows the given values of b with its corresponding area, calculated using its radius (r) using the equation Area = aorta. Table I: The damping coefficients values and the corresponding radii. Trial Area (AMA) Damping Coefficient Value (N*s/m) Damping Coefficient Uncertainty (N*s/m) 0. 0154 0. 021 187 0. 000224 0. 0234 0. 021648 0. 00302 0. 0314 0. 022879 0. 025907 0000207 The graph above shows that as the area Of the Object being oscillated was increased, the damping coefficient value increased as well. The positive correlation shown using the data in Table I is graphed below in Graph 5. Graph 5: The damping coefficient in relation to the Object’s area Results and Conclusions By looking at the results yielded during the experiment, observations of the effect that the change in the size of an object had on the air pressure could be made.

As the area increased, ranging from 0. 0154 m to 0,0415 m, the value of the damping coefficient increased as well, ranging from 0. 021187 N*s/m to 0. 025907 N*s/m, meaning that air pressure had a more significant effect on the larger objects. Either is less surface area on an object, it makes sense that it will meet less air resistance with a smaller exposed surface, therefore coming to a conclusion supported through the data given by the experiment.