Unformatted text preview: torque = d dt (angular momentum) ⇒ − `mg sin θ = d dt ± m` 2 dθ dt ² ⇒ − `mg sin θ = m` 2 d 2 θ dt 2 ⇒ d 2 θ dt 2 + g ` sin θ = 0 . 9. According to Problem 8, with ` = g , the function θ ( t ) satis±es the identity ( θ ) 2 2 − cos θ = C = const . (4.9) Our ±rst purpose is to determine the constant C . Let t a denote the moment when pendulum is in the apex point, i.e., θ ( t a ) = π . Since it doesn’t cross the apex over, we also have θ ( t a ) = 0. Substituting these two values into (4.9), we obtain 2 2 − cos π = C ⇒ C = 1 . 229...
View
Full Document
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Angular Momentum, magnitude mg sin

Click to edit the document details