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 electric potential at the midpoint between the two particles is 3.349 X 10⁻³ Volts
Explanation:
Electric potential is given as;
V = E*r
where;
E is the electric field strength, = kq/r²
V = ( kq/r²)*r
V = kq/r
k is coulomb's constant = 8.99 X 10⁹ Nm²/C²
q is the charge of the particles = 1.6 X 10⁻¹⁹ C
r is the distance between the particles = 859 nm
At midpoint, the distance = r/2 = 859nm/2 = 429.5 nm
V = (8.99 X 10⁹ * 1.6 X 10⁻¹⁹)/ (429.5 X 10⁻⁹)
V = 3.349 X 10⁻³ Volts
Therefore, the electric potential at the midpoint between the two particles is 3.349 X 10⁻³ Volts
Continent
jig-saw shapes when puzzled and combined together, formed one big continent -
Pangea, and was separated by drifts.
Fossil
comparisons of different species were discovered into two different, separated
continents in which when you combine them, they were one in the past.
Seismic,
volcanic, and geothermal activity are found along imagined plate
boundaries.
Plates
were actually rubbing against each other as evidence is seen on the formed
mountain ranges.
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Paleomagnetism,
magnetic field placement in the layers of the rock are present.</span>
Can be absorbed and transformed into heat. i know this because i used to work as a constructor for lights and i had to go over a training on this subject.
Answer:
The time is 176 seconds
Explanation:
We use the formula:
V= d/t V=velocity, d= distance, t= time
259 m/s= 45683 m/ t
t= 45683 m// 259 m/s
t= 176, 3 seg