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!!!!!!!!!!!

Question

mani_jha · Answer

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 · Answer

sorry for replying so late.ok,i understand but its not gonna be possible because we dont have t in the equation.

mani_jha · Answer

Actually t is there in 'wt'
$$dx/dt=Ad(sinwt)/dt$$
Did you notice the 't'? Now proceed

anonymous · Answer

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 · Answer

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 :)