Math Problem Solver

A block is attached to the end of a vertical spring, as shown in the figures. During an experiment, the block moves up and down in a periodic manner. At the beginning of the experiment, when the time is t=0 seconds, the block is at its maximum height, 4.5m above the floor (Figure 1). The block first reaches its minimum height, 1.5m above the floor, when t=4 seconds (Figure 2). When t=8 seconds, the block is back to its maximum height. The block continues to move up and down so that the block's height over time can be modeled by a sinusoidal function.

Let f(t) be the height of the block seconds t after the beginning of the experiment.