Simple Harmonic Motion

**Simplicity** · June 2nd 2008, 04:03 AM

Question:

Answer:

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

**bobak** · June 2nd 2008, 04:12 AM

Does the picture help?

Bobak

**earboth** · June 2nd 2008, 04:13 AM

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.

**mr fantastic** · June 2nd 2008, 04:15 AM

Originally Posted by Air

Question:

Answer:

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 ....

**bobak** · June 2nd 2008, 04:16 AM

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

**Simplicity** · June 2nd 2008, 04:23 AM

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

**bobak** · June 2nd 2008, 04:26 AM

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

**mr fantastic** · June 2nd 2008, 04:27 AM

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).

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