Introduction The mass moments of inertia of a rigid body with respect to a given axis of rotation is a measure of the geometrical distribution of the mass of a rigid body relative to that axis. It quantifies the resistance of the rigid body to rotate about the respective axis due to its mass and geometry. Dynamic modeling and control of the motion of a rigid body that experience rotational motion requires knowledge of its mass moments of inertia. Therefore, determining the mass moment of inertia of a rigid body is of a great importance. One of the methods to experimentally estimate the mass moments of inertial of a given object is to allow it to swing about a given axis of rotation. From recording the oscillatory motion, the mass moments of inertia could be estimated together with other dynamic parameters including the damping parameter. OOB lG G m Figure 1: A rigid body with irregular shape having oscillatory motion In this project you will build an oscillating pendulum with a given shape and you will use it to estimate the static and dynamic parameters of that shape. Arduino UNO will be used to log the motion data which will be picked up in the form of an analog signal using a tachometer sensor (a small dc motor). The signal that the tachometer generates is analog and is proportional to the rotational speed. Since the pendulum has clock-wise (CW) and counter-clock-wise (CCW) rotational motion, the measured signal by the tachometer will have positive and negative polarity. In order to interface the sensor with the Arduino, the analog signal coming from the sensor has to be scaled and shifted to fit within the available range of the analog to digital converter (ADC) of the Arduino (which is 0 to 5 volts). Required Tasks: To complete project each group need to perform the following tasks: 1) Using Newton-Euler formulation, find a mathematical model for the system in the form of a linear second order differential equation. 2) Solve the differential equation analytically to find (t), and differentiate (t) to find the angular velocity w(t). Assume that the pendulum is released from rest with a given initial angle 0. 3) Experimentally estimate the distance lg between the center of mass G and the center of rotation O (see Figure 1). 4) Design and build an Op Amp-based interfacing circuit to scale the analog signal and add to it an offset of 2.5 volts. 5) Use the Simulink support package for Arduino to log the data to a computer using Arduino UNO. 6) Experimentally measure the response when releasing the pendulum from rest with a given initial angle 0. 7) Use the collected data to estimate the dynamic parameters of the system. 8) Use the estimated parameters to simulate the system parameters. 9) Plot the simulated response and the actual response that is measured experimentally. 10) Write a report to summarize the work you did, and to compare the results and comment on the findings.