Answer Happy

4. As derived in class, a pendulum of length 1 released from rest at an angle 0, at t = 0 relative to the vertical equilibrium point has its angle (approximately] described in time by the formula 0(t) = 0, cos(w.t), where the angular frequency is w, = = (三 A) From the O(t) formula, find a formula for the angular speed of the pendulum, w(t). A reminder to avoid confusing the angular speed w and the angular frequency w, in this case. B) Find a formula for the angular acceleration of the pendulum alt). C) Based on your answers, find a formula for the magnitude of the tangential acceleration at(t). D) Based on your answers, find a formula for the magnitude of the centripetal acceleration ac(t). E) Consider the case where 0. = 1 radian and I = 1 meter. What is the period T of the oscillation in seconds? F) In this case, what are the values of 0, w, a, at, and ac at T/4 (44 way through the oscillation cycle)? Check that your values qualitatively make sense given the physical situation. G) In this case, what are the values of 0, w, a, at, and ac at T/2 (12 way through the oscillation cycle)? Check that your values qualitatively make sense given the physical situation.