Peoples Physics Book Version-2

11.4. Examples http://www.ck12.org

11.4 Examples

Example 1

Question: The effectivekof a diving board is 800N/m (we say effective because it bends in the direction of motion
instead of stretching like a spring, but otherwise behaves the same). A pudgy diver is bouncing up and down at the
end of the diving board. The y vs. t graph is shown below.

a) What is the distance between the lowest and the highest point of oscillation?

b) What is the y-position and velocity of the diver att=2?

c) What is the diver’s mass?

d) Write the sinusoidal equation of motion for the diver.

Solution:

a) As we can see from the graph the highest point is 2m and the lowest point is−2m. Therefore the distance is

|2m−(−2m)|=4m

b) To find the y-position we will use the equation

y=yi+Acos( 2 πf(t−ti))

First we must solve for the frequency. We know that

f=

1

T

From the graph we know that the period is 2 seconds, so the frequency is^12 hz. All we need to do now is plug in the
values to find the position att=2.

y=yi+Acos( 2 πf(t−ti)) = 0 + 2 ×cos(

2 π

2

( 2 − 0 ) = 2 ×cosπ× 2 =4m

To find the velocity we take the equation

v=− 2 πf Asin( 2 πf(t−ti))

and plug in the known values.

v=− 2 πf Asin( 2 πf(t−ti)) =

− 2 π

πs

×2m×sin(

2 π

πs

(2s−0s) = 3 .0m/s