Answer:
Explanation:
Given
Potential Energy is given by
![U(x)=ax^2+\frac{b}{x^2}](https://tex.z-dn.net/?f=U%28x%29%3Dax%5E2%2B%5Cfrac%7Bb%7D%7Bx%5E2%7D)
And Force is given by
![F=-\frac{\mathrm{d} U}{\mathrm{d} x}](https://tex.z-dn.net/?f=F%3D-%5Cfrac%7B%5Cmathrm%7Bd%7D%20U%7D%7B%5Cmathrm%7Bd%7D%20x%7D)
Particle will be at equilibrium when Potential Energy is either minimum or maximum
![F=-\left ( 2ax-\frac{2b}{x^3}\right )](https://tex.z-dn.net/?f=F%3D-%5Cleft%20%28%202ax-%5Cfrac%7B2b%7D%7Bx%5E3%7D%5Cright%20%29)
i.e.![ax=\frac{b}{x^3}](https://tex.z-dn.net/?f=ax%3D%5Cfrac%7Bb%7D%7Bx%5E3%7D)
![x_0=(\frac{b}{a})^{0.25}](https://tex.z-dn.net/?f=x_0%3D%28%5Cfrac%7Bb%7D%7Ba%7D%29%5E%7B0.25%7D)
So angular Frequency of small oscillation is given by
![\omega =\sqrt{\frac{U''(x)}{m}}](https://tex.z-dn.net/?f=%5Comega%20%3D%5Csqrt%7B%5Cfrac%7BU%27%27%28x%29%7D%7Bm%7D%7D)
for ![m=1](https://tex.z-dn.net/?f=m%3D1)
we get ![\omega =\sqrt{\frac{U''(x_0)}{1}}](https://tex.z-dn.net/?f=%5Comega%20%3D%5Csqrt%7B%5Cfrac%7BU%27%27%28x_0%29%7D%7B1%7D%7D)
![U''(x_0)=2a+6a= 8a](https://tex.z-dn.net/?f=U%27%27%28x_0%29%3D2a%2B6a%3D%208a)
![\omega =\sqrt{8a}](https://tex.z-dn.net/?f=%5Comega%20%3D%5Csqrt%7B8a%7D)
Gravity acts to influence the vertical motion of the projectile, thus causing a vertical acceleration. The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity.
Part A.
The forces are the same because the force from the smaller ball it transferring its Energy through the basketball and it's rebounding as Connecticut Energy back up to the smaller ball
Answer: When we use an analogy that represents the expanding universe with the surface of an expanding balloon, what does the inside of the balloon represent? The inside of the balloon does not represent any part of our universe.
A. Is very attractive. If it's sublimation directly from water vapor in the air to ice on the glass, then yes. But from liquid water mist to water ice, no. Ice is less dense than water. That's why cubes float in your soda. Better leave 'A' alone. . . . D. Ice pellets turn to liquid. That one's good.