Problem 2 A simple pendulum of length 1 and bob mass m swings back and forth with an effective weak damping coefficient, 7. The anchor can be driven to slide back and forth horizontally in simple harmonic motion with a maximum amplitude o. a) (4 points) If the horizontal position of the bob is x and the horizontal position of the slider is $, show that for small oscil- lations, the differential equation of motion for the bob is: sliding anchor 9 + 2y + 1 9 C 1 1 b) (2 points) If $(t) Co coswt, find expressions for the phase and amplitude of the steady-state oscillations in terms of wo, W, $o, and 7. 1 1 1 1 1 1 m c) (3 points) If it takes 50 swings for the amplitude to fall by a factor of e = 2.71828 ... when the pendulum is swinging freely (S0 = 0), find an expression for y in terms of wo. Is the assumption of weak damping justified? mg V Parts a, b, and c were done in the tutorial. You may use these results to answer the next three parts. -sliding anchor d) (4 points) Find numerical values for A/o and when the system is driven at: Tues 1 Wo i) w= 2 wo ii) w= = 2wo. 1 1 Note that you don't need to know g or l and thus wo! m X For phases, choose values for o such that 0)