P16_015.PDF

15. From highest level to lowest level is twice the amplitude x m of the motion. The period is related to the

angular frequency by Eq. 16-5. Thus, x m = 2 d and ω =0 . 503 rad/h. The phase constant φ in Eq. 16-3

is zero since we start our clock when x o = x m (at the highest point). We solve for t when x is one-fourth

of the total distance from highest to lowest level, or (which is the same) half the distance from highest

level to middle level (where we locate the origin of coordinates). Thus, we seek t when the ocean surface

is at x = 2 x m = 4 d .

x = x m cos( ωt + φ )

2 d cos(0 . 503 t +0)

4 d =

=cos(0 . 503 t )

which has t =2 . 08 h as the smallest positive root. The calculator is in radians mode during this

calculation.