If i know velocity, then i know acceleration right?

AI Thread Summary
In simple harmonic motion, the velocity of a particle can be expressed as v = ω√(A² - x²). To find acceleration, one can derive it from the velocity equation by substituting v = dx/dt and integrating to obtain the position function x(t) = A sin(ωt + θ). Once x(t) is determined, acceleration can be calculated as a(t) = dv/dt. The relationship between velocity and acceleration is further clarified through the application of energy conservation principles. Understanding these derivations is essential for analyzing motion in simple harmonic systems.
nemzy
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For velocity at a certain particle in a simple harmonic oscillation is the following:

v= w (anguluar frequency) times the squareroot of A^2-x^2

but if i wanted to find the acceleration at a certain particle in a simple harmonic oscillation, i can somehow derive a formula from the above equation right? But how would u derive it?

I know that that V= dx/dt ..and a= (d^2)x/dt^2

ugh, i forgot my calculus, anyone clear it up for me?

thanks
 
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for simple hamonic motion
x = A \sin{( wt-\theta)}
I have no idea what is your equation looks like

v= w (anguluar frequency) times the squareroot of A^2-x^2 :confused:

put it in Latex pls...
 
The equations for linear harmonic oscillator are something like that
x(t)=A\sin(\omega t+\phi)
v_{x}(t)=A\omega\cos(\omega t+\phi)
a_{x}(t)=-A\omega^{2}\sin(\omega t+\phi)

Then decide what are the initial conditions.And u can determine the 2 unknowns;

Daniel.
 
v= w \sqrt{A^2-x^2} is that what you trying to say?
 
OKAY, i don't know where did you get this equation... this is right but ppl usually don't write it this way, if you want to find a(t) from your equation, substitude v=dx/dt, you have
dt=dx/ (w \sqrt{A^2-x^2})
integrate both side and you will havex(t) = Asin(wt+\theta)
after you have x(t), everything should be easy
 
yes,

v= w \sqrt{A^2-x^2}

is what i am trying to say, so how can u derive a formula from the above equation for acceleration? that is my question
 
did i just tell you.. do the integral and find x(t)
after you have x(t), v(t)= dx/dt, a(t) = dv/dt
 
nemzy said:
yes,

v= w \sqrt{A^2-x^2}

is what i am trying to say, so how can u derive a formula from the above equation for acceleration? that is my question

The formula is deduced from applying the law of energy conservation.Once u integrate this ODE (using the method prescribed above),you need to diff.2 times wrt to time to find the acceleration.

Daniel.
 
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