Period of a Spring.doc

Period of a Spring EQUIPMENT 1 Equal Length Spring Set ME-8970 1 Force Sensor PS-2104 1 Motion Sensor PS-2103 1 Hooked Mass Set SE-8759 1 Xplorer GLX PS-2002 Required but NOT Included: 1 120 cm Rod ME-8741 1 45 cm Rod ME-8736 1 Large Table Clamp ME-9472 1 Multi-Clamp SE-9442 1 Metric Ruler  INTRODUCTION The purpose of this experiment is to find the relationship between the period and mass of a spring for small oscillations. The period of the spring and the spring constant are measured with a Force Sensor and a Motion Sensor. THEORY The period of a spring depends upon the spring constant and the mass: where T is the period, m is the mass and k is the spring constant. Squaring both sides of the equation and rearranging gives the following: The following sample graph of the period squared and the mass yields a linear slope of 4?2/k :  SETUP Setup the Large Table Clamp, 90 cm Rod, 45 cm Rod, and Multi-Clamp as in the picture to the right. Hang the Force Sensor from the 45 cm Rod so that the hook points directly downward. Tighten down the Force Sensor to the 45 cm Rod. Connect the Force Sensor to the GLX. Connect the Motion Sensor to the GLX. Move the switch at the top of the Motion Sensor to the “Cart” setting. Hang the red spring from the hook of the Force Sensor. Turn on the GLX by pressing the Power button. Press the “Zero” button on the Force Sensor. If necessary, press the Home Button on the GLX to return to the Home Screen. Press the button or navigate to the Sensors display. Use the buttons to select the Force Sensor. Change the Sample Rate to 50 as in the picture above. Change the Sample Rate to 50 for the Motion Sensor as well. Press the Home Button on the GLX to return to the Home Screen. Press to view the graph. PROCEDURE Hook a 200 g mass to the bottom loop of the spring. Record this value in kilograms in the Data Table below. If necessary, adjust the height so that the mass and Motion Sensor are at least 15 cm apart. (Hint