Thread: application 2

problem: A tersional pendulum is made by suspending a horizontal uniform metal disk by a wire from its center. If the disk is rotated and then released, it will execute simple(angular) harmonic motion. Suppose at t seconds the angular displacement of Ø radians from the initial position is given by the equation Ø = 0.2 cos [(pi)(t - 0.5)]. Determine, to the nearest tenth of a radian per second, how fast the angle is changing at 3.1 seconds.

Originally Posted by cazimi

problem: A tersional pendulum is made by suspending a horizontal uniform metal disk by a wire from its center. If the disk is rotated and then released, it will execute simple(angular) harmonic motion. Suppose at t seconds the angular displacement of Ø radians from the initial position is given by the equation Ø = 0.2 cos [(pi)(t - 0.5)]. Determine, to the nearest tenth of a radian per second, how fast the angle is changing at 3.1 seconds.

phi = cos(pi(t-0.5))

d phi/dt = -pi sin(pi(t-0.5))

so at t= 3.1:

d phi/dt = -pi sin(pi(2.6)) ~= -2.988 radians/s ~= -3.0 radians/s

RonL