Philosophy 2203E Chapter : Simple Ideas.docx

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rubydinosaur559

18 Jul 2012

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Though the qualities that affect our senses are so united and blended that there is no separation no distance between them. There is nothing can be plainer to a man than the clear and distinct perception he has of those simple ideas. Simple ideas, the materials of all our knowledge are suggested and furnished to the mind only by those two ways above mentioned viz sensation and reflection. When the understanding is once stored with these simple ideas it has the power to repeat compare and unite them even to an almost infinite variety and so can make at pleasure new complex ideas. Nor can any force of he understanding destroy those that are there. But can do nothing towards the making the least particle of new matter or destroying one atom of what is already being. That a blind man hath ideas of colours and a deaf man true distinct notions of sounds.

Related Questions

how does each frequency with 500 grams compare with thefrequencyfor the standing wave with the same number of anti-nodeswhen therewere 300 grams suspended from the end of thestring.

I don't understand if mass has any relation to frequency..I readinan article for a pendulum exp which was similar to this one,that"Mass doesn't affect the motion at all." However, from mylabresults the initial one for 1 anti-node, had a frequency of 13forthe 300 grams and 18 for the 500 grams, basically therewasslightly higher frequency for the 500 grams then the 300groups.How can I explain this scientifically? Thanks

Any ideas?

Thanks

A mass m rests on a frictionless horizontal table and isconnected to rigid supports via 2 identical springs each of relaxedlength L0 and spring constantk. Each spring is stretched to a length L considerable greater thanL0. Horizontal displacementsof m from its equilibrium position are labeled x and y.

(Diagram insert didn't work, all it really tells you is that xis on the axis of the springs and y is perpendicular to thesprings)

a) Write down the differential equation of motion (i.e.,Newton's Law) governing small oscillations in the xdirection.

b) Same as a but in the y direction (assume that y <<L).

c) In terms of L and L0, calculate the ratio of the periods ofthe oscillations along x and y.

d) If at t=0 the mass m is released from the point x = y = A0with zero velocity, what are its x and y coordinates at any latertime t?

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So, I started with just ma = -2kx for a, leading me to thedifferential equation x''(t) + (2k/m) x = 0.

Then I did basically the same thing with y.

However, when I get to c, there's my problem - I don't knowhow I could write any of this in L and L0.

Also, b doesn't really make sense to me because if y is smallwhen compared to L, it seems like there shouldn't be anyoscillation in the y direction.

The answer the back of the book shows for c and d are: