Harmonic Oscillation and Simple Harmonic Motion
Cyle, Stephanny, Alyssa
Goal: In this lab we use simple harmonic motion to evaluate the period of an object using a cart and two springs. The object’s period is measured against the theoretical value to examine the differences between the two values. The second part of the exam measures the oscillations of an object hanging from a spring. In this experiment we use Data Studio to find the value of the spring constant in order to calculate our unknowns.
Theory: An equation for theoretical period is given as T = 2π(m/k)1/2. In this equation T is equal to time for one complete oscillation, k is equal to spring constant, and m is the mass of the object moving back and forth. The direction of the force is opposite to the distance of the spring being stretched. Hooke’s Law states that the force of the spring is equivalent to the distance that the spring is compressed or stretched. In Data Studio we can plot the force vs. time in order to calculate the spring constant, K. In this activity there are two springs connected to a cart, therefore we simply add the two spring constants together. The equation would then be, T = 2π(m/k1+k2)1/2. The second part of the laboratory exercise deals with simple harmonic motion in which a mass oscillates on a spring. When a spring is at rest, without any force acting on it, it has a rest length denoted as L. A mass added to the spring will increase the Length by some value, ΔL. The change in distance is equal to L + ΔL. When the mass hanging from the spring is pulled downward the equation becomes F = -kx, where x is equal to the distance pulled downward and k is the spring constant. The period of oscillation is the same equation noted above. As the mass oscillated energy is converted back and forth from kinetic to some potential energy.
Procedure: Simple harmonic motion
In this part of the experiment we connected the Motion sensor to the SW700. We created two...