anonymous
  • anonymous
show that:(A=the squareroot of x^2+v^2/w^2)where w is the angular frequency,this is for simple harmonic motion.please help!!!!!!!!!!!
Physics
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SOLVED
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chestercat
  • chestercat
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Mani_Jha
  • Mani_Jha
Ok. Let's do this together. Let's take the equation: \[x=A \sin wt\] Differentiate this with respect to t and post your result. Can you do that?
anonymous
  • anonymous
sorry for replying so late.ok,i understand but its not gonna be possible because we dont have t in the equation.
Mani_Jha
  • Mani_Jha
Actually t is there in 'wt' \[dx/dt=Ad(sinwt)/dt\] Did you notice the 't'? Now proceed

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anonymous
  • anonymous
i know,but i,v noticed that differentiation wont lead us to get the correct A,so consider this equation:V=2pif(the squareroot of A^2-x^2).then,we can derive to get A.can u do so,because is also important to u.
Mani_Jha
  • Mani_Jha
Well that equation you want me to start with would result only after differentiation. \[v=Aw \cos wt=Aw \sqrt{1-\sin ^{2}wt }=Aw \sqrt{1-x ^{2}/A ^{2}}\] =\[v=w \sqrt{A ^{2}-x ^{2}}\] \[v ^{2}=w ^{2}(A ^{2}-x ^{2})\] Now make A the subject :)

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