Equipment List:
Introduction; This lab involves a graphical analysis of data taken during the simple harmonic motion of a glider when under the action of a spring's restoring force.
Theory: By examining the forces acting on the glider and using Newton's second law, a solution of the resulting differential equation is obtained with the condition that the angular frequency, , of the oscillating mass, m, is:
where k is the stiffness coefficient of the spring.
Since the period of the oscillation is defined as T 1/f and the angular frequency is defined as
= 2f, the relation between the period, the mass, and the stiffness can be found. Do this.
Note: Your photogate timer should be set for a 1ms resolution. Also, don't use the small hanging weight set found in the accessory box, use the weight and hanger set provided.
Procedure:
Refer to the diagram below for the set up.
Take sufficient data to analyze the relation between T and m. Use this data to draw a graph and find the stiffness of the spring k. Your graph should be linear but the relation between T and m is not linear. Construct the axes of your graph such that a linear graph will result. Relate the slope of the line to the value of k. Find the correct axes before you begin your data taking so that you can draw a rough graph while you take the data, point for point. This technique will help to see if your axes are indeed correct and if your data yields a straight line. Measure the slope of the graph and determine k.
More: Perform a linear regression for the value of k and a full uncertainty analysis for the absolute uncertainty in k. Include error bars on your data in the graph. Use the computer to draw a quality graph and tape the graph in your lab book.