Question

A buoy floating in the sea is bobbing in simple harmonic motion with amplitude 13 in and period 0.25 seconds. Its displacement d from sea level at time t=0 seconds is 0in, and initially it moves downward. (Note that downward is the negative direction.)Required:Give the equation modeling the displacement d as a function of time t.

Answer 1

Answer:

The equation is $x(t) = -13 cos (8 \pi t )$

Step-by-step explanation:

From the question we are told that

      The  amplitude is  $A = 13 \ in$

       The period is  $T = 0.25$

Generally the displacement function for a simple harmonic motion is mathematically represented as

        $x(t) = A cos (wt )$

Here  $w$ is the angular frequency which is mathematically represented as

          $w = \frac{2 \pi }{T}$

substituting values

          $w = \frac{2 \pi }{ 0.25}$

          $w = 8\pi$

Given that at t =  0  the displacement is equal to 0 it means that there is no phase shift and also  we are told that it is initially moving downward which implies that its Amplitude is  $A = -13\ in$

So the equation modeling the displacement d as a function of time t is mathematically represented as

          $x(t) = -13 cos (8 \pi t )$