1. (Non-dimensionalizing the linear pendulum equation Consider the linear pendulum equation: e(0)= 00, de /dt (0) = 2o L dt2 (a.) Find the simplest possible combination of L and g that yields dimension (sec)-1. Connbing L to get units Sec (b.) Let T new differential equation governing the linearized pendulum using the dimensionless time variable T. Also find the new initial conditions. How V9/L t. Carry out this change of variables to find the many parameter groupings are there now in the initial value problem? (c.) Let 0* = 0/00. Starting from the initial value problem obtained in part (b.), carry out this change of variables to obtain another new initial value problem governing the linearized pendulum. Update both the differential equation and the initial conditions. How many parameter groupings are there now in the initial value problem? (d.) Solve the initial value problem that you obtained in part (c.). Your answer will be in terms of 0* and T. (e.) As a check on your work, take your answer from part (d.) and rewrite it in terms of the original variables 0 and t. Check that this result satisfies the original initial conditions listed before part (a.).

1. (Non-dimensionalizing the linear pendulum equation Consider the linear pendulum equation: e(0)= 00, de /dt (0) = 2o L dt2 (a.) Find the simplest possible combination of L and g that yields dimension (sec)-1. Connbing L to get units Sec (b.) Let T new differential equation governing the linearized pendulum using the dimensionless time variable T. Also find the new initial conditions. How V9/L t. Carry out this change of variables to find the many parameter groupings are there now in the initial value problem? (c.) Let 0* = 0/00. Starting from the initial value problem obtained in part (b.), carry out this change of variables to obtain another new initial value problem governing the linearized pendulum. Update both the differential equation and the initial conditions. How many parameter groupings are there now in the initial value problem? (d.) Solve the initial value problem that you obtained in part (c.). Your answer will be in terms of 0* and T. (e.) As a check on your work, take your answer from part (d.) and rewrite it in terms of the original variables 0 and t. Check that this result satisfies the original initial conditions listed before part (a.).