4.0.1 Lab 10 - Torsion4.0.1.1 - Purpose4.0.1.2 - Background/Theory4.0.1.3 - Prelab4.0.1.4 - Equipment4.0.1.5 - Experimentalegr345 lab guide - 4.14.0.1 Lab 10 - Torsion4.0.1.1 - PurposeTo predicat and experimentally verify the period of oscillation for a torsional pen-dulum.4.0.1.2 - Background/Theory Suppose a large symmetric rotating mass has a rotational inertia J, and a twisting rod has a torsional spring coefficient K. Recall the basic torsional relationships.We can calculate the torsional spring coefficient using the basic mechanics of materialsFinally, consider the rotating mass on the end of a torsional rod.T∑T– Jα Jddt-----2θ===TK∆θ K θθ0–()==TJGθL----------=θh2d2d1h1T∑J1GL---------– θ Jddt-----2θ==egr345 lab guide - 4.24.0.1.3 - Prelab1. Calculate the equation for the natural frequency for a rotating mass with a tor-sional spring.2. Set up a Mathcad sheet that will- accept material properties and a diameter of a round shaft and determine the spring coefficient.- accept geometry for a rectangular mass and calculate the polar moment of inertia.- use the spring coefficient and polar moment of inertia to estimate the nat-ural frequency.- use previous values to estimate the oscillations using Runge-Kutta.- plot the function derived using the homogeneous and particular solutions.4.0.1.4 - EquipmentComputer with ...4.0.1.5 - Experimental1. 1. Calibrate the potentiometer so that the relationship between the output voltage and angle is known. Plot this on a graph and verify that it is linear before con-necting it to the mass.2. Set up the apparatus and connect the potentiometer to the mass. Apply a static torque and measure the deflected position. Use this to calculate a coefficient for the torsional spring.3. Apply a torque to offset the mass, and release it so that it oscillates. Estimate the natural frequency by counting cycles over a long period of time.4. Set up LabVIEW to measure the angular position of the large mass. The angular position of the mass will be measured with a potentiometer.5. Determine if the initial angle of deflection changes the frequency of oscillation.6. Compare the theoretical and experimental
View Full Document
Unlocking...