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I have two questions to ask and hopefully someone could help as im getting little help from my college and work collegues

1)The work done by an air compressor is given by

W = K [ (p1/p2)^(n-1/n) + (p1/p2)^(n-1/n)-2]

where p1,p2,n and K are all constants.

QUESTION - show that the work done is a minimum when p=sqrt(p1p2)

I have no idea where to start on this at all

2)motion of a particle performing damped vibrations is given by x=e^-t * sin 2t (x=displacement in metres and t=time in secs)

Find the times at which x is at a maximum and find the maximum distance for the least positive value of t. Find the acceleration at this point

I have found dx/dt and evaluated it for 0 This gives me an answer of t=31.6 (approx) but when i plug t=31.6 into dx/dt i come out with it equals 0, which suggests to me there is no maximum point but instead a point of inflection. That is about as far as i got on this question before i got stuck.

Any help on either of these question would be much appreciated as i have been trying to get my head around them for a while now with little or no success

Regards

Stuart

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# Motion of a particle performing damped vibrations

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