Hello. This is not a Physics homework problem, but rather a Programming project. I am asked to model a pendulum using the Java Swing class for graphics, but I'm having a few problems understanding the Physics behind it, and would appreciate a few answers and some guidance. Doing the research, I found some energy equations (K = 1/2*m*v^2; U = mgh), but I don't think they'll be too useful in my calculations. I then found the following equations: Omega (W) = SQRT(g/L), where Omega is the angular frequency, g is the acceleration due to gravity, and L is the length of pendulum the string. Theta (Angular Frequency) = Theta_MAX * cos(Omega * dt + Phi), where Theta is the angular distance moved in the given time period dt, Theta_MAX is the maximum angle for the pendulum, and Phi is the phase shift. I think I want to use the Theta equation for program, but I'm not sure how. Here are my initial assumptions for my model: * Bob starts from rest at an angle of 20 degrees (0.349 radians) * g = 10 m/s^2 * L = 100 m * dt = 0.1 sec (time increment for displaying the location of the bob at different intervals) Here are my calculations: Omega = SQRT(g/L) = SQRT(10/100) = 0.32 rad/s (approximately 18.33 degrees per second) Now here's where I think my calculations are incorrect when I try to find Theta, the angular displacement in each 0.1 second time increment. This angle will be used to draw the pendulum string (using the Java drawLine method). Theta = Theta_Max * cos(Omega * dt + Phi) Theta = 0.349 * cos(0.32 * 0.1 + 0.349) = 0.349 (??????????) It seems that in this equation, as the time increment dt approaches to 0, the angular displacement Theta moved in these 0 seconds approaches to 0.349 * cos(Omega * 0 + Phi) = 0.349 * cos(Phi) = 0.349 * cos(0 + 0.349) = 0.328 rad, which does not make sense. Am I mistaken with the phase shift? Or is the whole equation misplaced or something? I'm fairly sure this is the equation I need to figure out how far the bob has moved in each 0.1 second time increment. Any information on the matter will be greatly appreciated. Thank you.