Question

1) Consider a pendulum of constant length L to which a bob of mass m is attached. The Q6. pendulum moves only in a two-dimensional plane (see figure below). The polar frame of reference attached to the bob is defined by er,ce where er is the unit vector orientecd away from the origin and e completes the direct orthonormal basis. The pendulum makes an angle 0(t) between the radial direction and the vertical direction e(t) The position vector beinge ind the velocity and acceleration vectors [8 marks] 2) Initially, the bob is released from rest at an angle 0(t 0)We neglect the air resistance Writing Newton's second law along eo, show that the equation of motion for by: (t) is given Solve for θ(t). We assume that the variation of the angle is small and thus sin(θ) ~ θ. 12 marks]

Answer 1

dt dt olt 2

0 て 14 2 77 dlt 2 ㄥ