Answer:
The equation for the object's displacement is 
Explanation:
Given:
m = 16 lb
δ = 3 in
The stiffness is:
The angular speed is:
The damping force is:
Where
FD = 20 lb
u = 4 ft/s = 48 in/s
Replacing:
The critical damping is equal:
Like cc>c the system is undamped
The equilibrium expression is:
To find the ratio of planetary speeds Va/Vb we need the orbital velocity formula:
V=√({G*M}/R), where G is the gravitational constant, M is the mass of the distant star and R is the distance of the planet from the star it is orbiting.
So Va/Vb=[√( {G*M}/Ra) ] / [√( {G*M}/Rb) ], in our case Ra = 7.8*Rb
Va/Vb=[ √( {G*M}/{7.8*Rb} ) ] / [√( {G*M}/Rb )], we put everything under one square root by the rule: (√a) / (√b) = √(a/b)
Va/Vb=√ [ { (G*M)/(7.8*Rb) } / { (G*M)/(Rb) } ], when we cancel out G, M and Rb we get:
Va/Vb=√(1/7.8)/(1/1)=√(1/7.8)=0.358 so the ratio of Va/Vb = 0.358.
I couldnt type it out so here's a picture
atomic mass of carbon is C = 12 g/mol
atomic mass of hydrogen is H = 1 g/mol
now number of carbon atoms
Similarly the number of hydrogen atoms are
so Carbon atom and hydrogen atom must be in ratio of 10:30
so the ratio is 1:3
now the empirical formula is always in simplest form
