Answer:
Therefore the required solution is

Explanation:
Given vibrating system is

Consider U(t) = A cosωt + B sinωt
Differentiating with respect to t
U'(t)= - A ω sinωt +B ω cos ωt
Again differentiating with respect to t
U''(t) = - A ω² cosωt -B ω² sin ωt
Putting this in given equation


Equating the coefficient of sinωt and cos ωt
.........(1)
and

........(2)
Solving equation (1) and (2) by cross multiplication method


and 
Therefore the required solution is

The labeled points which is Letter B in the given Image is the point that the axis of rotation passes through. This problem is an example of rotational dynamics, formerly an object moves in a straight line then the motion is translational but when an object at inactivity lean towards to continue at inactivity and an object in rotation be possible to continue rotating with continuous angular velocity unless bound by a net external torque to act then is rotational. In a rotational motion, the entity is not treated as a constituent part but is treated in translational motion. It points out with the study of torque that outcomes angular accelerations of the object.
This approach is called the dimensional analysis which involves only the units of measurement without their magnitudes. You simply have to do the operations by using variables. Cancel out like items that may appear both in the numerator and denominator side. The solution is as follows:
F = mv²/r = [kg][m/s]²/[m] = [kg][m²⁻¹][1/s²] = [kg·m/s²]
We can solve the problem by using Snell's law, which states

where

is the refractive index of the first medium

is the angle of incidence

is the refractive index of the second medium

is the angle of refraction
In our problem,

(refractive index of air),

and

(refractive index of carbon disulfide), therefore we can re-arrange the previous equation to calculate the angle of refraction:

From which we find
Answer:
D. The requirement does not exist -the total electric flux is zero no matter what.
Explanation:
According to Gauss's law , total electric flux over a closed surface is equal to 1 / ε₀ times charge inside.
If charge inside is zero , total electric flux over a closed surface is equal to
zero . It has nothing to do with whether external field is uniform or not. For any external field , lines entering surface will be equal to flux going out.