Simple Harmonic Motion

• Jun 2nd 2008, 04:03 AM
Simplicity
Simple Harmonic Motion
Question:
http://i148.photobucket.com/albums/s...demic/SHMA.jpg

http://i148.photobucket.com/albums/s...demic/SHMQ.jpg

Problem:
I don't understand why they have used $\displaystyle -1$ as $\displaystyle x$ in part (b). Where did it come from? Thanks in advance.
• Jun 2nd 2008, 04:12 AM
bobak
Does the picture help?

Bobak
• Jun 2nd 2008, 04:13 AM
earboth
Quote:

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

I only can guess:

$\displaystyle 11\ am = -1\ pm$

According to the given results the argument of the function is time.
• Jun 2nd 2008, 04:15 AM
mr fantastic
Quote:

Originally Posted by Air
Question:
http://i148.photobucket.com/albums/s...demic/SHMA.jpg

http://i148.photobucket.com/albums/s...demic/SHMQ.jpg

Problem:
I don't understand why they have used $\displaystyle -1$ as $\displaystyle x$ 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 $\displaystyle x = 4 \cos \left( \frac{4 \pi}{25} t \right) {\color{red}+ 10}$.

Now substitute x = 9 ....
• Jun 2nd 2008, 04:16 AM
bobak
Quote:

Originally Posted by earboth
I only can guess:

$\displaystyle 11\ am = -1\ pm$

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

No x is displacement about the centre of oscillation.

Bobak
• Jun 2nd 2008, 04:23 AM
Simplicity
Also, the depth of $\displaystyle 9m$ is $\displaystyle 11 \ \mathrm{am}+3.6277 \ \mathrm{Hours} = 2.6277 \ \mathrm{pm}$. How did they convert that to $\displaystyle 2.38 \ \mathrm{pm}$?
• Jun 2nd 2008, 04:26 AM
bobak
Quote:

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

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
• Jun 2nd 2008, 04:27 AM
mr fantastic
Quote:

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

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).