Peoples Physics Book Version-2

http://www.ck12.org Chapter 11. Simple Harmonic Motion Version 2

Despite the fact that we have a negative value for the displacement(− 1 .3m)it makes sense that we would get a
positive velocity because, as we can see from the graph, the diving board is still moving down att=2.

c) To find the diver’s mass we will use the equation

T= 2 π

√

m

k

and solve form. Then it is a simple matter to plug in the known values to get the mass.

T= 2 π

√

m

k

⇒

T

2 π

=

√

m

k

⇒(

T

2 π

)^2 =

m

k

⇒k(

T

2 π

)^2 =m

Now we plug in what we know.

m=k(

T

2 π

)^2 = 800

N

m

(

πs

2 π

)^2 =200kg

d) To get the sinusoidal equation we must first decide whether it is a cosine graph or a sine graph. Then we must find
the amplitude (A), vertical shift (D), horizontal shift (C), and period (B). Cosine is easier in this case so we will work
with it instead of sine. As we can see from the graph, the amplitude is 2, the vertical shift is 0, and the horizontal
shift is−.4. We solved for the period already. Therefore, we can write the sinusoidal equation of this graph.

AcosB(x−C)+D= 2 cosπ(x+. 4 )