# Sinusoidal Graph Problem

#### ChiTown66

Homework for my Pre-Cal block A class...its cold up here in the north and I think my brain is frozen(Itwasntme)

Anyway, there is a lime-green pendulum that measures 16 inches from the top to the ball at the end of the string. The pendulum is 5 inches off the ground on a cinder block. The balls height is 8 inches off the ground at the following times: 2s, 4s...7s, 9s...So how high does the pendulum swing? (Wondering)

Also, the height from the ground to the top of the pendulum is 21 inches which I presume one could deduce from the info above...

#### Prove It

MHF Helper
Homework for my Pre-Cal block A class...its cold up here in the north and I think my brain is frozen(Itwasntme)

Anyway, there is a lime-green pendulum that measures 16 inches from the top to the ball at the end of the string. The pendulum is 5 inches off the ground on a cinder block. The balls height is 8 inches off the ground at the following times: 2s, 4s...7s, 9s...So how high does the pendulum swing? (Wondering)

Also, the height from the ground to the top of the pendulum is 21 inches which I presume one could deduce from the info above...
We're not supposed to provide full solutions to anything that counts towards your final grade (in other words, homework questions), but just as a hint, write the general sinusoidal function...

$$\displaystyle h = a\sin{(bt + c)} + d$$.

You have several $$\displaystyle (t, h)$$ points that lie on this curve, namely $$\displaystyle (0, 5), (2, 8), (4, 8), (7, 8), (9, 8)$$.

If you substitute these values in, you will be able to solve the equations simultaneously for $$\displaystyle a, b, c, d$$.

If you're really clever, you'll be able to find the period straight away, and the period = $$\displaystyle \frac{2\pi}{b}$$... so you could solve for $$\displaystyle b$$...