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Drongoski

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Re: 2009 3U Maths Marathon



Edit

Am I supposed to post a question ? I don't have one. Someone plz take over.
 
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lolokay

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Re: 2009 3U Maths Marathon

well i see no error in gurmies' working, and time =/= displacement
 

nerdsforever

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Re: 2009 3U Maths Marathon

1) An arithmetic series is 6.5, 9, 11.5, 14, 16.5 + .........

Find the sum of the first 500 terms.
 

Trebla

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Define the arithmetic mean of a set of numbers x1, x2, ...., xn as:

Show that:
 

Trebla

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Might've have been quicker to do:

:p

Question (relatively straightforward):

Recall that an object exhibits simple harmonic motion if:


Show that if a displacement x is a function consisting of a sum of sines and cosines of equal periods then it is simple harmonic, i.e. prove the following expression describes simple harmonic motion:

 
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azureus88

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In answer to Trebla's question:

[maths]x=\sum_{i=1}^{k}\sin(nt+\alpha _i)+\sum_{j=1}^{r}\cos(nt+\alpha_j)[/maths]

[maths]\frac{dx}{dt}=n\sum_{i=1}^{k}\cos(nt+\alpha _i)-n\sum_{j=1}^{r}\sin(nt+\alpha_j)[/maths]

[maths]\frac{d^2x}{dt^2}=-n^2(\sum_{i=1}^{k}\sin(nt+\alpha _i)+\sum_{j=1}^{r}\cos(nt+\alpha_j))[/maths]

[maths]=-n^2x[/maths]
 

studentcheese

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Nice and simple:

cos(@ + a) = cos@cosa - sin@sina

Derive the result for sin(@-a) using the above result.
 

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