Nov-28-2016: Lab - Physical Pendulum

LAB - Physical Pendulum

Tony Wu, Michell Kuang

November 28, 2016

Lab Goal: Derive expressions for the period of various physical pendulums.

Theory/Introduction: Objects will oscillate at different periods depending on the mass and shape of the object, as well as the point where it pivots.  We use small oscillations in order to take advantage of the small angle approximation of sin(theta) is approximately equal to (theta) for small angles.  This is helpful for when we need to calculate the angular speed and period.

Apparatus:  The triangle is hung with two paperclips so that it can be balanced as it oscillates.  A photogate sensor is placed at the bottom to record the period of oscillation for each object.

Experimental Procedure: In this lab we will determine the period of oscillation for three objects, a ring of finite thickness, a triangle pivoted at its apex, and a triangle pivoted as the midpoint of its base.  We set up the ring and derived expressions for the moment of inertia of the ring.  We assume that the point of pivot is exactly half way between the inner and outer radii.  We record the mass, dimensions, and the actual period of each object for small angle oscillations.  Below are the calculations for the expected period values of each object.

Data and Calculations: 

Conclusions: We had very accurate results when comparing our experimental values to our expected derived values.  Our values for the period of the ring were within 0.0108% error.  Our values for the period of the triangle pivoted at its apex were within 0.0124% error.  Lastly, our values for the period of the triangle pivoted about a midpoint at its base were within 0.653%.  Although the pivot clips added a small amount of mass to the shapes, because they are located slow close to the pivot, their inertia is basically negligible because the distance they are from the pivot is very small.  The masking tape would have a bigger effect, if any, on the measured moment of inertia because the masking tape is a much larger distance from the pivot, thus having a much larger effect on the inertia than the pivot clips.  Other sources of error can be from the fact that the shapes' dimensions weren't accurately measured.