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]
Chemical energy is the energy released or absorbed in a chemical reaction during the decomposition or formation of compounds
That's the definition but what was d? maybe I can help narrow it down
Explanation:
Below is an attachment containing the solution.
Answer: speed of light in solid = 1.88 * 10^8 m/s
Frequency is constant
Explanation: The relationship between the velocity of light wave and wavelength is given by the formulae below
V = fλ
During refraction, the frequency of light is constant, thus we have that
V = kλ which implies that velocity is proportional to wavelength.
Hence, we have that
v1/ λ1 = v2/ λ2
Where v1 = velocity of light in air = 3 * 10^8 m/s
v2 = velocity of sound in solid
λ1 = wavelength of light in air = 670nm
λ2 = wavelength of light in solid = 420nm
By making v2 subject of formulae, we have that
v2 = v1 * λ2/ λ1
v2 = 3 * 10^8 * 420nm/ 670nm
v2 = 3 * 10^8 * 0.6268
v2 = 1.88 * 10 ^8 m/s
b)
During refraction the frequency of light wave is constant this is because light consist of photons which has energy. it energy needs to be constant and for energy (E=hf) to be constant, frequency would be constant too.