You pull a simple pendulum 0.240 m long to the side through an angle of 3.50o and release it. (a) How much time does it take the pendulum bob to reach its highest speed? (b) How much time does it take if the pendulum is released at an angle of 1.75o instead of 3.50o?

Solution 45E The time period of a simple pendulum is given by = 2 g …..(1) Given, L = 0.240 m We know, g = 9.8 m/s 2 Substituting these values in equation (1), we get T = 2 09.80s T = 0.98 s (a) Now, the pendulum will have the highest speed when it is passing the equilibrium position. When the period is T. the pendulum will pass through the equilibrium at time T/4. Therefore, the time taken by the pendulum to reach its highest speed position is = T/4 = 0.98/4 s = 0.245 s 0.25 s (b) From equation (1), we find that the period of oscillation of the pendulum does not depend on the angle of release. So, even if the release angle is less in the second case, the pendulum will take approximate 0.25 s to reach the position of highest speed.