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m3 - shm

This is the question:

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The head of a piston moves with SHM of amplitude 0.1root 3m about a mean position O. How far from O is the head of the piston when it is travelling with a speed equal to half its maximum speed.

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Is there really enough information in the question to be able to do this?

Reply 1

Zacken

Original post by maggiehodgson

AFAIK, yes. Why do you think there isn't? Call the maximum speed v. Then

v^2 = w^2 \times 0.1^2 \times 3

Then you want to find x s.t

\frac{1}{2}\sqrt{w^2 \times 0.1^2 \times 3} = \sqrt{w^2 (0.1^2 \times 3 - x^2)}

(or something vaguely like that)

Reply 2

TeeEm

Original post by Zacken

AFAIK, yes. Why do you think there isn't? Call the maximum speed v. Then

v^2 = w^2 \times 0.1^2 \times 3

Then you want to find x s.t

\frac{1}{2}\sqrt{w^2 \times 0.1^2 \times 3} = \sqrt{w^2 (0.1^2 \times 3 - x^2)}

(or something vaguely like that)

AFAIK??

Reply 3

Zacken

Original post by TeeEm

AFAIK??

As far as I know

Reply 4

TeeEm

Original post by Zacken

As far as I know

danke

Reply 5

maggiehodgson

Original post by Zacken

AFAIK, yes. Why do you think there isn't? Call the maximum speed v. Then

v^2 = w^2 \times 0.1^2 \times 3

Then you want to find x s.t

\frac{1}{2}\sqrt{w^2 \times 0.1^2 \times 3} = \sqrt{w^2 (0.1^2 \times 3 - x^2)}

(or something vaguely like that)

Yes, you are dead right. I just hadn't gone far enough with my own work to see how to eliminate w.

Reply 6

Zacken

Original post by maggiehodgson

Yes, you are dead right. I just hadn't gone far enough with my own work to see how to eliminate w.

Great. Yeah, that's always a thing with these questions, lots of terms cancel out. Especially in stuff like circular motion where mass cancels out at the very last step and you breathe a sigh of relief.

Reply 7

maggiehodgson

Original post by Zacken

Thanks for the warning - I think that's the next chapter. Oh Joy!

Reply 8

Zacken

Original post by maggiehodgson

Thanks for the warning - I think that's the next chapter. Oh Joy!

It's a fun one, to be honest. The 'show that' questions are a free 6/8 marks. Enjoy it, make sure you know your energy principles well.

Reply 9

maggiehodgson

Original post by Zacken

It's a fun one, to be honest. The 'show that' questions are a free 6/8 marks. Enjoy it, make sure you know your energy principles well.

Believe it or not I'm only doing mechanics for fun. I'm a mature student, self teaching. I did A level - also self taught - two years ago. Having been out of education and exams for many many years I almost scared myself to death and wished I'd never put myself through the terror of the exam room. I swore I'd never do such a thing ever again.

So mechanics for fun. I must be a masochist.

Reply 10

Zacken

Original post by maggiehodgson

I can relate with the self-teaching thing, seems like you're doing good, from what I've seen of you so far! So keep at it. Being a masochist is fun. Are you planning on doing M4/5 as well?

Reply 11

maggiehodgson

Original post by Zacken

I can relate with the self-teaching thing, seems like you're doing good, from what I've seen of you so far! So keep at it. Being a masochist is fun. Are you planning on doing M4/5 as well?

Well. We'll see. At the current rate of progress I might not even get to the end of M3 hahahha.

However, if I do, given that beating my head on a brick wall is preferable to daytime tv/housework/statistics/decision mats etc, then probably yes.

Thanks for the encouragement. Without TSR it would have to be daytime TV and housework. God forbid.