A) ![x=\pm \frac{A}{2\sqrt{2}}](https://tex.z-dn.net/?f=x%3D%5Cpm%20%5Cfrac%7BA%7D%7B2%5Csqrt%7B2%7D%7D)
The total energy of the system is equal to the maximum elastic potential energy, that is achieved when the displacement is equal to the amplitude (x=A):
(1)
where k is the spring constant.
The total energy, which is conserved, at any other point of the motion is the sum of elastic potential energy and kinetic energy:
(2)
where x is the displacement, m the mass, and v the speed.
We want to know the displacement x at which the elastic potential energy is 1/3 of the kinetic energy:
![U=\frac{1}{3}K](https://tex.z-dn.net/?f=U%3D%5Cfrac%7B1%7D%7B3%7DK)
Using (2) we can rewrite this as
![U=\frac{1}{3}(E-U)=\frac{1}{3}E-\frac{1}{3}U\\U=\frac{E}{4}](https://tex.z-dn.net/?f=U%3D%5Cfrac%7B1%7D%7B3%7D%28E-U%29%3D%5Cfrac%7B1%7D%7B3%7DE-%5Cfrac%7B1%7D%7B3%7DU%5C%5CU%3D%5Cfrac%7BE%7D%7B4%7D)
And using (1), we find
![U=\frac{E}{4}=\frac{\frac{1}{2}kA^2}{4}=\frac{1}{8}kA^2](https://tex.z-dn.net/?f=U%3D%5Cfrac%7BE%7D%7B4%7D%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7DkA%5E2%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B8%7DkA%5E2)
Substituting
into the last equation, we find the value of x:
![\frac{1}{2}kx^2=\frac{1}{8}kA^2\\x=\pm \frac{A}{2\sqrt{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dkx%5E2%3D%5Cfrac%7B1%7D%7B8%7DkA%5E2%5C%5Cx%3D%5Cpm%20%5Cfrac%7BA%7D%7B2%5Csqrt%7B2%7D%7D)
B) ![x=\pm \frac{3}{\sqrt{10}}A](https://tex.z-dn.net/?f=x%3D%5Cpm%20%5Cfrac%7B3%7D%7B%5Csqrt%7B10%7D%7DA)
In this case, the kinetic energy is 1/10 of the total energy:
![K=\frac{1}{10}E](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B10%7DE)
Since we have
![K=E-U](https://tex.z-dn.net/?f=K%3DE-U)
we can write
![E-U=\frac{1}{10}E\\U=\frac{9}{10}E](https://tex.z-dn.net/?f=E-U%3D%5Cfrac%7B1%7D%7B10%7DE%5C%5CU%3D%5Cfrac%7B9%7D%7B10%7DE)
And so we find:
![\frac{1}{2}kx^2 = \frac{9}{10}(\frac{1}{2}kA^2)=\frac{9}{20}kA^2\\x^2 = \frac{9}{10}A^2\\x=\pm \frac{3}{\sqrt{10}}A](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dkx%5E2%20%3D%20%5Cfrac%7B9%7D%7B10%7D%28%5Cfrac%7B1%7D%7B2%7DkA%5E2%29%3D%5Cfrac%7B9%7D%7B20%7DkA%5E2%5C%5Cx%5E2%20%3D%20%5Cfrac%7B9%7D%7B10%7DA%5E2%5C%5Cx%3D%5Cpm%20%5Cfrac%7B3%7D%7B%5Csqrt%7B10%7D%7DA)
They differ from each other<span> in wavelength. Wavelength is the distance between </span>one wave<span> crest to the next. </span>Waves<span> in the </span>electromagnetic<span> spectrum vary in size from very long radio </span>waves<span> the size of buildings, to very short gamma-rays smaller </span>than<span> the size of the nucleus of an atom.</span>
Calderas are what sometimes surround it
Answer:
cold cathode fluorescent lamp
Explanation:
A cold cathode fluorescent lamp (CCFL) is a lighting system that uses two phenomena: electron discharge and fluorescence.
CCFLs are mainly used as light sources for backlights, since they are compact and durable than ordinary fluorescent lamps. They exhibit a wide range of brightness and color (color temperature and chromaticity) that can be achieved by varying the pressure and type of the material injected into the glass tube. The thickness and type of the phosphor used to coat the inner wall of the tube also plays a role in altering the color and brightness.
A barometer is a scientific instrument used to measure atmospheric pressure, also called barometric pressure. The atmosphere is the layers of air wrapped around the Earth. That air has a weight and presses against everything it touches as gravity pulls it to Earth. Barometers measure this pressure.