Data Collection
Table 1. Change in Velocity Of A Horizontal Spring – Mass System Over Time. The data was collected with the motion sensor provided.
Table 2. The Kinetic Energy at the Peak of Each Oscillation. The values chosen were at the peak of each oscillation. Because there were 7 peaks, 7 values were chosen. Kinetic energy was calculated by using f(x) =
Data Processing
Graph 1. The Change in Velocity Of A Horizontal Spring – Mass System Over Time. The uncertainties for both velocity and time were too small to be seen and were excluded from the graph. We must, however, take into consideration that they are there. A bigger version of this graph will be attached at the end of this lab.
Graph 2. The Change in the Kinetic Energy Over Time. The uncertainties were too small to be seen and were excluded from the graph. We must, however, take into consideration that they are there. A bigger version of this graph will be attached at the end of this lab.
Calculating the Kinetic Energy
Calculation of the Rate of Energy Loss
Analysis
Our hypothesis on how the graph would look proved to be correct. The graph shows the general trend for a horizontally oscillating spring-mass system. The trend shows that as time passes by, the velocity of the spring changes goes up, then down, then back up again. This is when the mass is pulled to its maximum displacement (amplitude), and when the mass is released, it begins oscillating with a displacement that never exceeds this distance. The greater the amplitude, the more energy the system has. At maximum displacement, the restoring force is at a maximum value, and therefore, so is the acceleration of the mass. When the mass is released, it accelerates from rest toward its equilibrium position. As the mass approaches this position, its velocity is increasing. But the restoring force is decreasing because the spring is not stretched as much. As the mass returns to its equilibrium position, it achieves its maximum velocity. It is moving toward the left (negative direction), but the restoring force acting on it is zero because its displacement is zero. The mass continues to move through the equilibrium position and begins to compress the spring mass-system. As it does this, the restoring force acts on the mass toward the right (positive direction) to return it to its equilibrium position. This causes the mass to slow down, and its velocity approaches zero. After passing through the equilibrium position, the mass experiences a restoring force that opposes its motion and brings it to a stop at the point of maximum compression. Its amplitude here is equal, but opposite of its amplitude when it started. At maximum displacement, the velocity is zero. The restoring force has reached its maximum value again. The restoring force is positive, and the displacement is negative. The restoring force again accelerates the mass toward the equilibrium. The mass has accelerated on its way to the equilibrium position where it is now. The restoring force and acceleration are again zero, and the velocity has achieved the maximum value toward the right. At equilibrium, the mass is moving to the right. The mass has returned to the exact position where it was released. Again the restoring force and acceleration are negative and the velocity is zero. The oscillation then repeats this cycle. The reason for the wave-like pattern in the graph is because the spring does not instantly stop when it reaches the maximum/minimum point – it keeps on bouncing left and right, which then results in the graph continuously going up and down in a wave-like motion.
Evaluation
The experiment was successful in providing a graph which displayed the relationship between velocity (m/s) and time (s) for a horizontally oscillating spring-mass system. The graph shows that as time increases, the velocity of the horizontal spring-mass system decreases gradually (from about 1.03 m/s to 0.12 m/s). Therefore, we can conclude that there is a net loss in energy from the system ( J per second), which is caused by friction, which slows down the spring-mass and decreases the velocity. The wave-like pattern in the graph is caused when the spring-mass system is released from its maximum displacement; the restoring force pulls it to towards the opposite side (since velocity is a vector, this produces a negative velocity), and then back again to its beginning point, slowing down slightly due to friction. A major source of error came from the air resistance and friction, which caused the spring-mass system to gradually slow. In reality, due to simple harmonic motion, the system would continue to oscillate for an infinite period of time. However, to completely eliminate this friction would be very difficult; though the effects of friction were reduced by the air being forced under the spring to create an “air-hockey” effect. To improve on this further, I would recommend lubricants on the surfaces in contact (the rail and spring). There will always be air resistance in this experiment. If these issues are rectified, then future experiments concerning this method of experimentation will provide more accurate results.
