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How does different oscillating masses and spring constants affect the time needed to complete a constant number of oscillation in a simple harmonic motion.

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Introduction

How does different oscillating masses and  spring constants affect the time needed to complete a constant number of oscillation in a simple harmonic motion.

 Aim of investigation. To determine what kind of effect would the varying of the mass of the oscillating object as well as the spring constant have on the time needed to complete a certain amount of oscillation in a simple harmonic motion (SHM). Hypothesis Depending on the changes made on the oscillating mass and the different kinds of springs with different spring constant (K) used the time needed should vary either increase or decrease. Materials used Springs with different values of spring constants (K), different masses, a weigh, stop watch, ruler, and a stand. Variables There are three variables in this experiment.The independent variable is the ones that we vary to see its effect on the dependent variable i.e. oscillating mass and spring constant.The dependent variable is time. It varies according to the changes in the independent variable. The controlled variables are the number of oscillation, the displacement of the spring(x), gravity. Methods for controlling variables. Before starting the experiment, to get results as accurate as possible the controlled variables should remain controlled. This includes having the oscillating mass constant when measuring the effect of spring constant on time and vice versa. The displacement (the distance from which the spring is pulled from the equilibrium point) should also remain constant throughout each of the experiments. This can be done using a ruler and pulling the spring to a certain length.The number of oscillations should be the same throughout the experiment. Method of experiment. First, the stand was placed on a horizontal surface. Then For the first experiment, where the oscillating mass is varied, a spring is chosen and attached to the stand. Then different masses were attached to the spring. A ruler was used to measure the length of the spring with the mass on. After that, the spring was stretched 5cm from its equilibrium position and released. Using a stopwatch, the time taken for complete 10 oscillations was recorded. For each mass used there were four attempts.For the second experiment, where the spring constant is varied to see the effect on time, the spring constant of each spring was determined. This was done using hook’s law, which will be explained further in the discussion part. After finding the spring constant of four different spring a constant mass, 100g, was attached on them. The spring with a mass on were stretched 5 cm from its equilibrium position and released. This was done for the different masses. Using a stopwatch, the time taken for 10 complete oscillations was recorded. For each spring constant, there were four trials.

Middle

9.41±0.1

9.41±0.1

9.43±0.1

9.44±0.1

9.42±0.5

0.15

10.41±0.1

10.41±0.1

10.41±0.1

10.44±0.1

10.41±0.5

Table 1.1 time taken to fulfill 10 oscillations in a simple harmonic motion using different masses.

Graph 1.1 time taken for different masses to perform 10 oscillations

B. The same oscillating mass but different spring constant.

 Spring constant (Nm-1) Time(sec) Mean value (sec) 4.65±1 9.32±0.1 9.32±0.1 9.53±0.1 9.53±0.1 9.42±0.1 5.88±1 8.59±0.1 8.66±0.1 8.68±0.1 8.78±0.1 8.67±0.1 9.09±1 6.75±0.1 6.82±0.1 6.85±0.1 6.87±0.1 6.82±0.1 25.00±1 4.09±0.1 4.09±0.1 4.09±0.1 4.22±0.1 4.12±0.1

Table 1.2 time taken for a mass of 100g to complete 10 oscillations using different springs with different spring constants.

Graph 1.2 time taken for 0.1 kg mass to complete 10 oscillations using different spring constants

Discussion: - all vibrating system undergoes the same motion repeatedly. Oscillations are very common phenomena in all areas of physics. And this experiment deals with a very special periodic oscillation called simple harmonic motion (SHM). There are different types of simple harmonic motions. This experiment focuses on a simple harmonic motion with a mass at the end of a vertical spring. In order to say that a motion is a simple harmonic motion it must fulfill two things. First, there must be a fixed equilibrium position and secondly when the mass is moved away from the equilibrium the acceleration of the particle must be proportional to the amount of the displacement and opposite in direction.

Conclusion

………………………….hook’s law where f is force

K is spring constant

X is displacement

From this, the spring constant can be written as-

………………………………………………… equation one

By attaching an object of mass 0.1 kg, the force on the spring will be 1 N because the weight of the object is one. Then by subtracting the difference in length of the spring after 0.1 kg mass was attached X can be found. By applying equation one K can be calculated.

 Spring (No) Displacement (X) without mass attached (cm) Displacement (X) with mass attached (cm) Difference (cm) Value of spring constant(K) (Nm-1) by applying Eq. one 1 6.5±1 28.0±1 21.5±1 4.65±1 2 16.0±1 33.0±1 17.0±1 5.88±1 3 16.0±1 27.0±1 11.0±1 9.09±1 4 17.0±1 21.0±1 4.0±1 25.0±1

Table 1.3 spring constant (K) values for springs used in this experiment.

Conclusion: - it can be concluded that by increasing the mass the time taken (period) to complete oscillations will increase. On the other hand, having the same mass and thereby increasing the spring constant (K) decreases the time taken (period).

Limitations: - when the spring is attached to the stand, there is no way to make sure that it stays linear all the time. In addition, the number of oscillations can be missed as they are counted.

Improvements: - a video camera with high resolution can be used to count the number of oscillations. Side supports can be used to keep the spring linear.

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