Simple Harmonic Motion
Simple Harmonic Motion
Ethan Albers
Case Western Reserve University, Department of Physics
Cleveland, OH 44106
Abstract:
In this lab, my partner and I observed oscillations that were translational and rotational. The two forms we studied must have a form of a restoring force that is proportional to the displacement of the object from its point of equilibrium. This produces the harmonic motion which this lab wants. At small and big amplitudes we measured/observed the translational oscillation of the spring. To go with this also, we measured it when it had the spring had added mass and when it didn’t have added mass. Additional to this, we were able to measure the rotational oscillation of a Torsion pendulum that was rotating on its central axis. With this data we created a sine curve to display the oscillating effect which was made possible by using the translational oscillation. After that, my partner and I created a histogram that displayed the different lengths of the period of oscillation. This histogram used the Torsion pendulum to make the graph. In both of these mini labs, they displayed the principle of the oscillating effect that is produced by a restoring force.
Spring Mass Oscillator:
Introduction and Theory: The way translational harmonic motion is illustrated is by the oscillation with the spring. The compression and the extension of the spring while it oscillates, shows there is a force that is applied relative to the equilibrium position, x0, and then at a different position x. (1)
In this equation, K represents the spring constant of the given spring. Additionally, in the lab we added a mass, m, to the system. So we can use an equation that will illustrate the harmonic motion: (2) (3) (4)
In the equation we have the amplitude which is represented by A, and then the frequency of the spring which is, then the phase angle which is, and then lastly x0 which is the equilibrium position. The
Ethan Albers
Case Western Reserve University, Department of Physics
Cleveland, OH 44106
Abstract:
In this lab, my partner and I observed oscillations that were translational and rotational. The two forms we studied must have a form of a restoring force that is proportional to the displacement of the object from its point of equilibrium. This produces the harmonic motion which this lab wants. At small and big amplitudes we measured/observed the translational oscillation of the spring. To go with this also, we measured it when it had the spring had added mass and when it didn’t have added mass. Additional to this, we were able to measure the rotational oscillation of a Torsion pendulum that was rotating on its central axis. With this data we created a sine curve to display the oscillating effect which was made possible by using the translational oscillation. After that, my partner and I created a histogram that displayed the different lengths of the period of oscillation. This histogram used the Torsion pendulum to make the graph. In both of these mini labs, they displayed the principle of the oscillating effect that is produced by a restoring force.
Spring Mass Oscillator:
Introduction and Theory: The way translational harmonic motion is illustrated is by the oscillation with the spring. The compression and the extension of the spring while it oscillates, shows there is a force that is applied relative to the equilibrium position, x0, and then at a different position x. (1)
In this equation, K represents the spring constant of the given spring. Additionally, in the lab we added a mass, m, to the system. So we can use an equation that will illustrate the harmonic motion: (2) (3) (4)
In the equation we have the amplitude which is represented by A, and then the frequency of the spring which is, then the phase angle which is, and then lastly x0 which is the equilibrium position. The
References: 1. Driscoll, D., General Physics I: Mechanics Lab Manual, CWRU Bookstore, Spring 2013