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# M3 Simple Harmonic Motion, finding that time.

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1. So basically Q4 iv) OCR MEI M3 January 2010.

All parts before part iv) were fine.

Now I am going to go through my new thoughts on the situation and hopefully some bodies may confirm, reject or adjust my thinking.

So to find the time taken, I started with finding the equation which describes the motion:
Simple enough.

Then to find the displacement when , I used the renowned formula:

Found that
Now inputting this newfound into the first formula, followed by rearrangement gave:

Originally I would think to divide by 5.6 to get a straight forward answer for t, knowing that this is the time taken for the particle to reach a velocity of the first time.
However, now thoughts are beginning to rearrange themselves, new patterns are being seen and new found wisdom kicks in... From looking at the mark scheme.

So if I let , and look at a normal cosine graph with period , I can find the point where I can see is going downwards.

Seeing that the particle is going downwards with , just past the point where or (depends on the way you swing), I have found that the particle travels downwards with when .

Using the substitution from earlier ( ), I can now find the time by reverting back to the original cosine function.

Therefore,

I am also no longer a LaTeX virgin.

So, yay or nay?
2. (Original post by Wunderbarr)

So, yay or nay?
Yay.

You could have differentiated and got/used

for a more direct method.
3. I've just done the question and a simpler method I found was to use to find the time to travel up then add this to a quarter of the period. Let Y be the point this happens at. This gives us the time to get from A to Y (OR from Y to A) hence the time we need is the period - (time taken to go from Y to A).

I hope that made sense but it seems more straight forward to me personally in the way I work with these problems, I hope it's perhaps helped?
4. (Original post by ghostwalker)
x
Oh yes, I can see why that may be a more direct method.

Thanks, I will consider that way, as well as my own.

(Original post by Foutre en L'air)
x
Soz Oz, but it's not as straight forward for me >_< . But I think our ideas are quite similar.

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