# Physics II forgotten equation (oscillations)

• PCSL
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.
PCSL
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 $v=w{\sqrt{A^2x^2}}$ comes from? Thank you.

Last edited:
That equation can't be correct. The units on the RHS work out to be length2/time.

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:

$\frac{1}{2}mv_x^2 + \frac{1}{2}kx^2=\frac{1}{2}kA^2$

$mv_x^2 + kx^2=kA^2$

Try solving for the velocity.

vela said:
Try solving for the velocity.
You get $v={\sqrt{{\frac{k}{m}}A^2x^2}}$ which is equivolaent to $v=w{\sqrt{A^2x^2}}$.

No, you don't. How'd you get that?

vela said:
No, you don't. How'd you get that?

$mv_x^2 + kx^2=kA^2$

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.

Yup, that's the equation I think you were looking for.

## 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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