Question

A pendulum is a weight attached to a fixed rod, as shown in the figures. Suppose that during an experiment, a pendulum moves back and forth in a periodic manner. At the beginning of the experiment , when the time is t = 0 seconds , the pendulum is at a point halfway between its maximum and minimum distances from the wall, 2.5 m away from the wall (Figure 1) and moving toward the wall. The pendulum first reaches its minimum distance from the wall , 1 m from the wall , when t = 1 second (Figure 2). When t = 4 seconds, the pendulum is back to a point halfway between its maximum and minimum distances from the wall. The pendulum continues to move back and forth so that the distance between the pendulum and the wall over time can be modeled by a sinusoida ! function .

Answer 1

Yes, a pendulum is a weight attached to a fixed rod that swings back and forth in a periodic motion. The distance between the pendulum and the wall can be modeled by a sinusoidal function, where the distance between the pendulum and the wall is represented by the equation d(t) = 2.5 + 1 sin ((π/2)t). As shown in the figures, when t = 0 seconds, the pendulum is at a point halfway between its maximum (2.5 m away from the wall) and minimum distances (1 m away from the wall), and when t = 1 second, the pendulum reaches its minimum distance from the wall. The pendulum continues to move back and forth so that when t = 4 seconds, it is back to a point halfway between its maximum and minimum distances from the wall.