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

Answer:
The energy stored in the capacitor is 333.3 J
Explanation:
Energy stored in a capacitor = CV²/2
C = capacitance = 14 × 10⁻⁶F
V = 6.90 × 10³V
Energy = (14 × 10⁻⁶)(6.90 × 10³)²/2 = 333.27 = 333.3 J
Hope this Helps!!!
Answer:
Electric field at a distance of 1.45 cm will be 
Explanation:
We have given the distance d = 1.45 cm = 0.0145 m
And the potential difference 
There is a relation between potential difference and electric field
Electric field at a distance d due to a potential difference is given by
, here E is electric field, V is potential difference and d is distance
So 
Using the equation v(avg)=distance/time
and the equation v=v(original)+a(t)
solve for acceleration
2600=0+a(12)
a=216.66666 m/s^2
Then, you use the equation
v^2=v(original)+2a*(change in x)
2600^2=2(216.666666)*change in x
6760000/2/216.666666 = 15600 meters which is the length of the race
Then using v(avg)=x/t
15600/12= 1300 m/s
Answer:
exponential
Explanation:
type of function that describes the amplitude of damped oscillatory motion is exponential because as we know that here function is
y = A ×
× cos(ωt + ∅ ) ..................................... ( 1 )
here function A ×
is amplitude
as per equation ( 1 )it is exponential
so that we can say that amplitude of damped oscillatory motion is exponential