Peoples Physics Concepts

10.1. Harmonic Period and Frequency http://www.ck12.org

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)We know that

f=

1

T

From the graph we know that the period is 2 seconds, so the frequency is^12 hz.

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 choose whether to go with 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 )