In the system shown in the figure, the masses and springs are identical. System in vertical axis oscillates. The weights of objects and springs and the position potential
Lagrange the equation (s) of motion of the system, neglecting its energies
using the method. Also determine the frequency equation of the system.
(The objects move according to the equation x = sbt. coswt and that the friction
accept it is not).

To place a communications satellite into a geosynchronous orbit at an altitude of 22,240 mi above the surface of the earth, the satellite first is released from a space shuttle , which is in a circular orbit at an altitude of 185 mi, and then is propelled by an upper-stage booster to its final altitude. as the satellite passes through a, the booster's motor is fired to insert the satellite into an elliptic transfer orbit. the booster is again fired at b to insert the satellite into a geosynchronous orbit. knowing that the second firing increases the speed of the satellite by 4810ft/s, determine (a.) the speed of the satellite as it approaches b on the elliptic transfer orbit, (b.) the increase in speed resulting from the first firing at a.