do u know the answer to this question yet
Answer:
The function is x = e^(-t/2) * (0.792*sin12t + 5cos12t)
Explanation:
we have to:
m = mass = 4 kg
k = spring constant = 577 N/m
c = damping constant = 4 N*s/m
The differential equation of motion is equal to:
m(d^2x/dt^2) + c(dx/dt) + k*x = 0
Replacing values:
4(d^2x/dt^2) + 4(dx/dt) + 577*x = 0
Thus, we have:
4*x^2 + 4*x + 577 = 0
we will use the quadratic equation to solve the expression:
x = (-4 ± (4^2 - (4*4*577))^1/2)/(2*4) = (-4 ± (-9216))/8 = (1/2) ± 12i
The solution is equal to:
x = e^(1/2) * (c1*sin12t + c2*cos12t)
x´ = (-1/2)*e^(1/2) * (c1*sin12t + c2*cos12t) + e^(-t/2) * (12*c1*cos12t - 12*c2*sin12t)
We have the follow:
x(0) = 5
e^0(0*c1 + c2) = 5
c2 = 5
x´(0) = 7
(-1/2)*e^0 * (0*c1 + c2) + e^0 * (12*c1 - 0*c2) = 7
(-1/2)*(5) + 12*c1 = 7
Clearing c1:
c1 = 0.792
The function is equal to:
x = e^(-t/2) * (0.792*sin12t + 5cos12t)
Answer:
The sun's mass moved toward the outer edge of it
Explanation:
Answer:
cos to = $ 24
Explanation:
When replacing the bulb only 25% of the energy is used, therefore
W = 0.25 100
W = 25 W
Let's look for the energy in the life of the bulb
E = 25 10⁻³ 12000
E = 300 Kwh
now we can calculate the cost using a direct proportion rule.
Cost = 0.08 300
cos to = $ 24
Answer:
a) 915 m
b) 0.15 W/
Explanation:
solution:
a) The wavelength of the microwaves electromagnetic wave is:
λ=
=
=0.025 m
the circular radar antenna acts like a circular aperture of diameter D will have a bright central maximum of diameter:
w=2.44λL/D
so at 30 km screen:
w=2.44λL/w
=2.44*0.025*30*10^3/2
=915 m
b)
The area of a beam at 30 km is:
A=
=
=
=
the average microwave intensity is equal to the ratio of the power of the antenna and area of the beam:
I=P/A
So at 30 km:
I=100*10^3/657*10^3
=0.15 W/
