Physics II forgotten equation (oscillations)

In summary, the conversation discusses the derivation of the equation v=w{\sqrt{A^2x^2}} and its units. The equation is found in the book and comes from the conservation of energy formula. The conversation also includes a step-by-step process for solving for the velocity in the equation.
  • #1
PCSL
146
0
I am reviewing for a test on oscillations and I have no clue how I derived a formula I used for my homework.

Could anyone help me figure out where the equation [itex]v=w{\sqrt{A^2x^2}}[/itex] comes from? Thank you.
 
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  • #2
That equation can't be correct. The units on the RHS work out to be length2/time.
 
  • #3
vela said:
That equation can't be correct. The units on the RHS work out to be length2/time.

I actually just found the equation in the book, it comes from the conservations of energy formula. I don't understand how it can work for the same reason you listed, that's why I am confused. And I'm 100% sure I am copying it down correctly.

It is derived from:

[itex]\frac{1}{2}mv_x^2 + \frac{1}{2}kx^2=\frac{1}{2}kA^2[/itex]

[itex]mv_x^2 + kx^2=kA^2[/itex]
 
  • #4
Try solving for the velocity.
 
  • #5
vela said:
Try solving for the velocity.
You get [itex]v={\sqrt{{\frac{k}{m}}A^2x^2}}[/itex] which is equivolaent to [itex]v=w{\sqrt{A^2x^2}}[/itex].
 
  • #6
No, you don't. How'd you get that?
 
  • #7
vela said:
No, you don't. How'd you get that?

[itex]mv_x^2 + kx^2=kA^2[/itex]

Sorry, I'm not going to use latex for this so I can do it faster.

mv^2=kA^2-kx^2

v^2=(kA^2-kx^2)/m

v^2= (k/m)(A^2-x^2)

v=sqrt((w^2)(A^2-x^2))

v=w(sqrt(A^2-x^2))

I think that was actually beneficial for me typing that out lol.
 
  • #8
Yup, that's the equation I think you were looking for.
 

Related to Physics II forgotten equation (oscillations)

What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A * sin(ωt + φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

How do you calculate the period of an oscillation?

The period of an oscillation can be calculated using the equation T = 2π/ω, where T is the period and ω is the angular frequency.

What is the equation for calculating the frequency of an oscillation?

The equation for calculating the frequency of an oscillation is f = 1/T, where f is the frequency and T is the period.

What is the difference between simple harmonic motion and damped harmonic motion?

Simple harmonic motion is the motion of an object back and forth along a straight line, while damped harmonic motion is when the amplitude of the oscillation decreases over time due to an external force acting on the object.

How do you find the maximum velocity of an oscillating object?

The maximum velocity of an oscillating object can be found by taking the derivative of the displacement equation, x = A * sin(ωt + φ), with respect to time and setting it equal to zero. This gives us vmax = A * ω, where vmax is the maximum velocity and ω is the angular frequency.

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