SHM Physics Lab 1 Upload To Site
Simple Harmonic Motion
Objective
The purpose of this experiment was to investigate the different variables describing simple harmonic motion (SHM) using a spring-mass system in vertical oscillation. We measured the position and velocity of the spring-mass system under different conditions in order to extract parameters used to describe SHM such as amplitude, frequency, and phase. We tested whether the predicted behaviour based on our mathematical model of SHM was cohesive with the observed parameters in the experiment. We also used Hooke’s Law to measure the spring characteristic, k, spring constant, in order to model energy of SHM and determine if energy is conserved via transfer between potential and kinetic.
Simple harmonic motion is a mathematical model for many forms periodic motion such as sound waves within a medium, a pendulum, and electrons in matter. French mathematician Jean Baptiste made the first description of SHM in 1822.
Theory
Simple harmonic motion (SHM) is a motion where the force applied on an object is constantly directed towards the equilibrium point and is proportional to the position of the object relative to the equilibrium position [3]. The restoring force that is created from displacement from equilibrium is directly related to the displacement, and is modelled using the Hooke’s Law [2]:
F=-kx
In this equation k is the spring constant in Newtons per meter (N/m), F is the restoring force in Newtons (N), and x is the displacement of the object. This force causes an object to oscillate about the equilibrium position as a sinusoidal function of time. Position of an object in SHM can be found using the equation below [3]: x(t)= A sin (2πft + )
In this equation, A is amplitude of the sinusoidal function in centimeters, f is the frequency in hertz, t is the time in seconds, and Φ is the phase constant in radians. Energy in simple harmonic motion oscillates back and forth between potential and kinetic energy. By ignoring
Objective
The purpose of this experiment was to investigate the different variables describing simple harmonic motion (SHM) using a spring-mass system in vertical oscillation. We measured the position and velocity of the spring-mass system under different conditions in order to extract parameters used to describe SHM such as amplitude, frequency, and phase. We tested whether the predicted behaviour based on our mathematical model of SHM was cohesive with the observed parameters in the experiment. We also used Hooke’s Law to measure the spring characteristic, k, spring constant, in order to model energy of SHM and determine if energy is conserved via transfer between potential and kinetic.
Simple harmonic motion is a mathematical model for many forms periodic motion such as sound waves within a medium, a pendulum, and electrons in matter. French mathematician Jean Baptiste made the first description of SHM in 1822.
Theory
Simple harmonic motion (SHM) is a motion where the force applied on an object is constantly directed towards the equilibrium point and is proportional to the position of the object relative to the equilibrium position [3]. The restoring force that is created from displacement from equilibrium is directly related to the displacement, and is modelled using the Hooke’s Law [2]:
F=-kx
In this equation k is the spring constant in Newtons per meter (N/m), F is the restoring force in Newtons (N), and x is the displacement of the object. This force causes an object to oscillate about the equilibrium position as a sinusoidal function of time. Position of an object in SHM can be found using the equation below [3]: x(t)= A sin (2πft + )
In this equation, A is amplitude of the sinusoidal function in centimeters, f is the frequency in hertz, t is the time in seconds, and Φ is the phase constant in radians. Energy in simple harmonic motion oscillates back and forth between potential and kinetic energy. By ignoring
References: [1] Knight, Radall Dewey. "Oscillations." Physics for Scientists and Engineers: A Strategic Approach. 3rd ed. San Francisco: Pearson, 2013. 378-400. Print. [2] "Forces and Elasticity." BBC News. BBC, n.d. Web. 26 Jan. 2015. <http://www.bbc.co.uk/schools/gcsebitesize/science/add_aqa/forces/forceselastic ityrev2.shtml>. [3] Asadi, Masoud, Zeydabadi. "Damped Simple Harmonic Motion." D Scientific Research Publishing Inc., Mar. 2014. Web. 26 Jan. 2015. [4] “The Damped Harmonic Oscillator.” The University of Arizona. Web. 27 Jan. 2015 < http://www.physics.arizona.edu/physics/gdresources/documents/12_Damped_Harmonic%20_Oscillator.pdf >