Answer Happy

10. Consider the governing differential equation for the Simple Pendulum, for small a approximation (Equation (5) in the Introduction Section): de dt2 L = For the experiment performed the initial conditions are: (0) = 0 , 6(0) = 0 a. Use MATLAB to do the following, considering the Steel Pendulum: Obtain the analytical solution for the above differential equation in terms of g, 1 and 00. The solution obtained must appear similar to that obtained by hand (in Question 1). b. Substitute the following parameter values in the solution obtained in part (a): 1 = 0.7 m, g= 9.81 m/s, 0(0) = 15 0(0) = 0. AERO 350 Page 7 of 8 Lab Experiment No. 1 c. Obtain a plot of the solution 0(t) obtained in part (b), for time 0 to 10 seconds. d. For the plot obtained in part (c), why do the oscillations have the same amplitude throughout? Is this what is observed with the oscillations of the simple pendulum on the Universal Vibration Apparatus? Explain. e. From the solution obtained in part (b), what is the natural frequency of oscillations of the simple pendulum (in rad/s)? How was this value found? Show your working. f. Use the value of natural frequency of oscillations (obtained in part (e)) in order to find the Time Period of oscillations of the simple pendulum in seconds). g. Find the absolute percent error between the Time Period value obtained in part (f) and the Experimental Time Period value in the Results Table (corresponding to the same value of pendulum length used in part (b), i.e., for I = 0.7m).