searches to consider an ideal soring whose mass is negligtibke and the coefficient of spring is k. the end of one of the springs is tied to an object with mass m. the ibject was intially given a drift initial X0 and intial mimentum P0 and then released so that it moves to the left and right periodically on the x-axis without experiencing any friction. the hamiltonian of this system can be written as :

H =p^2/2' + 1/2kx

using taylor's equation description in poisson parentheses, which can be written as :

show that

*() = x(0) + t{x, H}aplezo + {{x,H), H}ap le-o + {x, H), h), i) lw + p(t) = p(0) + t{p, Haplt-o + 3} {{p,H),H)ple-+5 {{{p,H),1), h), ple+ 22 13 Buktikanlah bahwa: Po X(t) = x, cos wt + -sin wt b. p(t) = P, cos wt mwx, sin wt a. mo *() = x(0) + t{x, H}aplezo + {{x,H), H}ap le-o + {x, H), h), i) lw + p(t) = p(0) + t{p, Haplt-o + 3} {{p,H),H)ple-+5 {{{p,H),1), h), ple+ 22 13 Buktikanlah bahwa: Po X(t) = x, cos wt + -sin wt b. p(t) = P, cos wt mwx, sin wt a. mo