M3 further dynamics question Watch

sulexk
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#1
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#1
A particle P moves along the x-axis in such a way that time t seconds its distance x metres from origin O is given by x=6cos((PI)t/4)

a) show that the particle is moving with shm

The rest (b) (c) and (d) I have done already.

But how do I show this?

Shall I say that x=acos(wt+ B) and compare?
saying that a=6 w=(PI/4) and B=0?

Is this acceptable?

Thank you?
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warwickorbristol
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#2
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You need to prove that acceleration is proportional to displacement in the opposite direction.

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x(double dot) = -kx
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sulexk
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#3
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(Original post by warwickorbristol)
You need to prove that acceleration is proportional to displacement in the opposite direction.

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x(double dot) = -kx
in this case how would I do that since they only gave me the equation?

Thank you
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sulexk
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#4
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Perhaps I must differentiate twice?
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warwickorbristol
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Differentiate it twice to find acceleration (The rate of rate of change of displacement), then substitute in x for the cos((PI)t/4) part. You should have acceleration is equal to minus the displacement x some constant, then just drop the constant and replace equals with proportional.
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warwickorbristol
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Yep bang on
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sulexk
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Thank you!
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