HSC 2016 MX1 Marathon (archive) (1 Viewer)

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hedgehog_7

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Re: HSC 2016 3U Marathon

A particle moves in simple harmonic motion with period 8pi. Initially, it is at the point P where x = 4 moving with velocity v =6. Find, correct to three significant figures, how long it takes to return to P:

by expressing the motion in the form x = b sin nt + c cos nt and using the t formulae.

so essentially ive found the displacment formuale to be x = 24 sin (t/4) + 3 cos (t/4) but im not sure what the question is asking me to do nor use the t method. when it asks for how long it returns to P does it want me to let x = 4 in the formulae that i have just found and to solve for t? and if so ,how do i use the t method to do this.

The answer is t = 8 (tan inverse 6) = 11.2 ish

many thanks!!
 
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parad0xica

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Re: HSC 2016 3U Marathon

Nailgun said:
Not sure about what level of education, but he does have a particularly intense hatred for a certain HS tutoring centre
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Interesting claim. Could you reveal your reasoning? Or identify the premises.
 
leehuan

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Re: HSC 2016 3U Marathon

hedgehog_7 said:
A particle moves in simple harmonic motion with period 8pi. Initially, it is at the point P where x = 4 moving with velocity v =6. Find, correct to three significant figures, how long it takes to return to P:

by expressing the motion in the form x = b sin nt + c cos nt and using the t formulae.

so essentially ive found the displacment formuale to be x = 24 sin (t/4) + 3 cos (t/4) but im not sure what the question is asking me to do nor use the t method. when it asks for how long it returns to P does it want me to let x = 4 in the formulae that i have just found and to solve for t? and if so ,how do i use the t method to do this.

The answer is t = 8 (tan inverse 6) = 11.2 ish

many thanks!!
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Shouldn't it be x = 24sin(t/4) + 4cos(t/4)?
 
Nailgun

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Re: HSC 2016 3U Marathon

parad0xica said:
Interesting claim. Could you reveal your reasoning? Or identify the premises.
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parad0xica said:
Guys, this is the consequence of being heavily influenced by NGO & SONS.
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parad0xica said:
Ayyyy, this guy knows what's up

I had a feeling you go to NGO & SONS based on your past arrogance but it was just intuition...
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parad0xica said:
Have you interacted with every single one in your class or enough people to make that claim? Do you think most people at NGO & SONS are easily influenced?

I had Mai and he was a bad person. He knows that and is trying to fix it.

What is the true meaning of life? I would like to know ^_^
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Q.E.D
 
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leehuan

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Re: HSC 2016 3U Marathon

hedgehog_7 said:
Yes it is sorry my bad... do you know what i have to do afterwards?
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Firstly, t = 8 tan^-1(6) is wrong. Try substituting it into the original equation and you get something that's not 0.
I tried this with both 4cos(t/4) AND 3cos(t/4)

So we want when the particle returns to P, which is x=4. Therefore simply let x=4

4 = 24sin(t/4) + 4cos(t/4)
1 = 6sin(t/4) + cos(t/4)

At this point, without the slightest of hesitation bombard with the auxiliary angle method:

1 = sqrt(37)sin(t/4 + tan^-1(1/6))

I'll leave it here, and wait for you to comment first
 
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hedgehog_7

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Re: HSC 2016 3U Marathon

well the cambridge book stated at the end that the answers was t = 8 tan^-1(6) so became confused as to what i was trying to solve. the question is stating for x=4 right?
 
leehuan

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Re: HSC 2016 3U Marathon

Should've mentioned earlier that this was a Cambridge question so that I could've had something to refer to.







Note: arctan just means tan^-1


I will leave part b) for you to do yourself first.
 
kawaiipotato

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Re: HSC 2016 3U Marathon

Prove that a+b< c*sqrt(2) if a,b are two sides of a right angled triangle and c is the hypotenuse.
 
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InteGrand

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Re: HSC 2016 3U Marathon

Yeah, in fact there's equality if and only if the right-triangle is isosceles.
 
Carrotsticks

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Re: HSC 2016 3U Marathon

Paradoxica said:
obviously true by inspection

note this is only true if the sides are not the same length.
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For the spirit of this thread, perhaps you'd like to actually answer the questions rather than providing what is more commonly known as 'proof by intimidation'.

Yes, many of these can be done by inspection, good for you. But the reality is that there are several processes that go on in our heads to produce the result. We still follow some train of thought when doing something as menial as factorising quadratics. People want to see and follow this train.

Remember that people read these forums and learn from the solutions. But what can they learn when all they see is you waving around your maths dick all over the Maths forum? You add little to no value to the forum by providing such answers.
 
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