Kinematics
How the object moved
The object moved by the unbalanced force of gravity and the spring. The force of gravity on the mass is constant throughout the whole harmonic motion. The force of the spring gets stronger as the mass moves from the highest position to the equilibrium position to the lowest position and back to the highest position to start over. This movement of force is what caused the mass to move in a harmonic motion.
The object moved by the unbalanced force of gravity and the spring. The force of gravity on the mass is constant throughout the whole harmonic motion. The force of the spring gets stronger as the mass moves from the highest position to the equilibrium position to the lowest position and back to the highest position to start over. This movement of force is what caused the mass to move in a harmonic motion.
Position vs. time graph for one period
![Picture](/uploads/3/8/8/0/38804569/54196_orig.png)
The graph shows that the height of the mass started at one point and decreased after a few tenths of a second and then moved back up to another point. The position of the mass was at negative at the highest point then negative at the lowest point and negative at the equilibrium. The shape of the graph is a full parabola.
Velocity vs. time graph for one period
![Picture](/uploads/3/8/8/0/38804569/4991926_orig.png)
The shape of the graph does not make a full parabola. On my graph a few points after 0 was not plotted and a few points before 0.8 seconds was not plotted either. On the first half of the motion the mass had negative velocity. The mass on the spring is at the highest point where the velocity is -1.0.The mass is about to come down to go the equilibrium point. The mass of the spring is at the equilibrium point where the velocity is about -1.6. The force of gravity acting on the mass will still push the mass down to the lowest point. The mass of the spring is at the lowest point where the velocity is about -2.5. During the second half of the motion the mass had positive velocity. The velocity increased after the lowest point was reached. If I would have showed a longer time period for the harmonic motion then a full parabola would be present.
Acceleration vs. time graph for one period
Calculation of the spring constant
![Picture](/uploads/3/8/8/0/38804569/5920083_orig.png)
Spring Constant
According the Hooke's law, the force required to stretch or compress the spring and it will be directly proportional to the amount of stretch.
hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
According the Hooke's law, the force required to stretch or compress the spring and it will be directly proportional to the amount of stretch.
hyperphysics.phy-astr.gsu.edu/hbase/hframe.html