Given:
k = 100 lb/ft, m = 1 lb / (32.2 ft/s) = 0.03106 slugs
Solution:
F = -kx
mx" = -kx
x" + (k/m)x = 0
characteristic equation:
r^2 + k/m = 0
r = i*sqrt(k/m)
x = Asin(sqrt(k/m)t) + Bcos(sqrt(k/m)t)
ω = sqrt(k/m)
2π/T = sqrt(k/m)
T = 2π*sqrt(m/k)
T = 2π*sqrt(0.03106 slugs / 100 lb/ft)
T = 0.1107 s (period)
x(0) = 1/12 ft = 0.08333 ft
x'(0) = 0
1/12 = Asin(0) + Bcos(0)
B = 1/12 = 0.08333 ft
x' = Aω*cos(ωt) - Bω*sin(ωt)
0 = Aω*cos(0) - (1/12)ω*sin(0)
0 = Aω
A = 0
So B would be the amplitude. Therefore, the equation of motion would be x
= 0.08333*cos[(2π/0.1107)t]
Answer:
According to the second law of thermodynamics, we are unable to use the heat of the ocean and the atmosphere because we do not have a reservoir that has a temperature lower than the ocean or the atmosphere.
Explanation:
As you already know, the ocean and atmosphere have a lot of thermal energy, however, we are unable to convert this energy into mechanical energy that would be useful for our activities. This can be explained by the second law of thermodynamics, since it states that the presence of two bodies with different temperatures is necessary for it to be possible to transform heat into work.
In this case, to transform the thermal energy of the ocean and the atmosphere into mechanical energy we would need the existence of a thermal motor, which is only possible to be established when there is a body with high thermal energy and a sink, a reservoir, with low thermal energy, which will be the place where the heat will be expelled, to be converted into work. We do not have a reservoir with less thermal energy than the ocean and the atmosphere, so we cannot use their energy.
Answer:
electric
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