# Math Help - Simple Harmonic Motion

1. ## Simple Harmonic Motion

Question:

Problem:
I don't understand why they have used $-1$ as $x$ in part (b). Where did it come from? Thanks in advance.

2. Does the picture help?

Bobak

3. Originally Posted by Air
...
I don't understand why they have used $-1$ as $x$ in part (b). Where did it come from? Thanks in advance.
I only can guess:

$11\ am = -1\ pm$

According to the given results the argument of the function is time.

4. Originally Posted by Air
Question:

Problem:
I don't understand why they have used $-1$ as $x$ in part (b). Where did it come from? Thanks in advance.
Their model is incomplete.

The correct model (taking t = 0 to correspond to 11:00 am) is $x = 4 \cos \left( \frac{4 \pi}{25} t \right) {\color{red}+ 10}$.

Now substitute x = 9 ....

5. Originally Posted by earboth
I only can guess:

$11\ am = -1\ pm$

According to the given results the argument of the function is time.
No x is displacement about the centre of oscillation.

Bobak

6. Also, the depth of $9m$ is $11 \ \mathrm{am}+3.6277 \ \mathrm{Hours} = 2.6277 \ \mathrm{pm}$. How did they convert that to $2.38 \ \mathrm{pm}$?

7. Originally Posted by Air
Also, the depth of $9m$ is $11 \ \mathrm{am}+3.6277 \ \mathrm{Hours} = 2.6277 \ \mathrm{pm}$. How did they convert that to $2.38 \ \mathrm{pm}$?
3.6277 hours is 3 hours 37 minutes and 39 seconds.

look for a button like the one i circled on your calculator, that will do the conversion.

Bobak

8. Originally Posted by Air
Also, the depth of $9m$ is $11 \ \mathrm{am}+3.6277 \ \mathrm{Hours} = 2.6277 \ \mathrm{pm}$. How did they convert that to $2.38 \ \mathrm{pm}$?
Think of 2.6277 as degrees .... The 0.6277 then converts to 37 minutes and 39.72 seconds ...... (Remember that 1 hour = 60 minutes and 1 minute = 60 seconds which is why the angle analogy works).