(normalized oscillator dynamics) consider a damped spring–mass system with dynamics mq¨+ cq˙ + kq = f. let ω0 = p k/m be the natural frequency and ζ = c/(2√km) be the damping ratio. a) show that by rescaling the equations, we can write the dynamics in the form q¨+ 2ζω0q˙ + ω2 0q = ω2 0u, (3.39) where u = f/k. this form of the dynamics is that of a linear oscillator with natural frequency ω0 and damping ratio ζ. b) show that the system can be further normalized and written in the form

answer: 802.3 kilo joules of energy represents 191.75 kilo calorie of energy.

explanation:

energy released during combustion of one mole methane = 802.3 kilo joules

if 1 kilo joule = 0.239006   kilo calorie

then ,802.3 kilo joule will be = 802.30.239006 kilo calorie

802.3 kilo joule = 191.75 kilo calorie

hence, the energy in kilo calorie is 191.75 kilo calorie.

prolly a beacuse the momentuem the car has increases while going down hill

vapour or gas assuming atmospheriv pressure

get the total number of pieces of fruit and divide it by 4 to get the average. the result is the answer to the problem. 14 total number of fruits and there are 4 members. 14 divided by 4 is equals to 3.5.