Answer:
Explanation:
Using second degree taylor polynomials
let
be position function and set 
where S(0) is the initial position
Then
and 
we have
, 
so 
b.) yes
D
Explanation:
The are the same but difference
- The net force is greatest at the position of maximum displacement
- The net force is zero when at the equilibrium position
Explanation:
The motion of a spring is a Simple Harmonic Motion, in which the displacement of the end of the spring is given by a periodic function of the form

where A is the amplitude (the maximum displacement), and
the angular frequency of the motion.
We can analyze the net force acting on the spring by looking at Hooke's law:

where
F is the net force
k is the spring constant
x is the displacement
From the equation, we notice immediately that:
- The net force is the greatest when the displacement x is the greates, so at the position in which the spring has maximum compression or stretching
- The net force is zero when the displacement x is zero, so when the spring crosses the equilibrium position
Learn more about forces:
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E S *
The "E" represents Earth, "S" represent Sun, and the "*" represents the nearest star(which is Proxima Centauri).
The main thing to worry about here is units, so ill label everything out.
D'e,s'(Distance between earth and sun) = .<span>00001581 light years
D'e,*'(Distance between earth and Proxima) = </span><span>4.243 light years
Now this is where it gets fun, we need to put all the light years into centimeters.(theres alot)
In one light year, there are </span>9.461 * 10^17 centimeters.(the * in this case means multiplication) or 946,100,000,000,000,000 centimeters.
To convert we multiply the light years we found by the big number.
D'e,s'(Distance between earth and sun) = 1.496 * 10^13 centimeters<span>
D'e,*'(Distance between earth and Proxima) = </span><span>4.014 * 10^18 centimeters
</span>
Now we scale things down, we treat 1.496 * 10^13 centimeters as a SINGLE centimeter, because that's the distance between the earth and the sun. So all we have to do is divide (4.014 * 10^18 ) by (<span>1.496 * 10^13 ).
Why? because that how proportions work.
As a result, you get a mere 268335.7 centimeters.
To put that into perspective, that's only about 1.7 miles
A lot of my numbers came from google, so they are estimations and are not perfect, but its hard to be on really large scales.</span>
Answer:
The value is 
Explanation:
From the question we are told that
The diameter of the ring is 
The length of the solenoid is 
The diameter of the solenoid is 
The number of turns is N = 1500
The change in current in the solenoid is 
The time taken is 
Generally the radius of the ring is

=> 
=> 
Generally the area of the ring is mathematically represented as

=>
=> 
Generally the induced emf is mathematically represented as

Here

Here
is the permeability of free space with value

So

=> 
So

=> 