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This question is incomplete, the complete question is;
Write the differential equation that governs the motion of the damped mass-spring system, and find the solution that satisfies the initial conditions specified. Units are mks; γ is the damping coefficient, with units of kg/sec
m = 0.2, γ = 1.6 and k = 4
Initial displacement is 1 and initial velocity is -2
x" + _____ x' ____x = 0
x(t) =
Answer:
the solution that satisfies the initial conditions specified is;
x(t) = +
Explanation:
Given the data in the question ;
m = 0.2, γ = 1.6, k = 4
x(0) = 1, x'(0) = -2
Now, the differential equation that governs the motions of spring mass system is;
mx" + γx' + kx = 0
so we substitute
0.2x" + 1.6x' + 4x = 0
divide through by 0.2
x" + 8x' + 20x = 0
hence, characteristics equation will be;
m² + 8m + 20 = 0
we find m using; x = [ -b±√(b² - 4ac) ] / 2a
m = [ -8 ± √((8)² - 4(1 × 20 )) ] / 2(1)
m = [ -8 ± √( 64 - 80 ) ] / 2
m = [ -8 ± √-16 ) ] / 2
m = ( -8 ± 4i ) / 2
m = -4 ± 2i
Hence, the general solution of the differential equation is;
x(t) = +
From the initial conditions;
c₁ = 1, c₂ = 1
the solution that satisfies the initial conditions specified is;
x(t) = +
Answer:
D. The moon is closer to Earth than the sun.
Explanation:
Tides are formed as a consequence of the differentiation of gravity due to the moon across to the Earth sphere.
Since gravity variate with the distance:
(1)
Where m1 and m2 are the masses of the two objects that are interacting and r is the distance
For example, see the image below, point A is closer to the moon than point b and at the same time the center of mass of the Earth will feel more attracted to the moon than point B. Therefore, that creates a tidal bulge in point A and point B.
The Sun tidal force contributes to the tidal force of the moon over the earth making high tides higher and low tides lower.
However, even when the sun is more massive than the moon, it is farther away from the Earth than the moon. So, it is clear by equation 1 that the moon's gravity has a greater effect on Earth's oceans than the sun's gravity.
