Question

and part b
solve the initial value problem for the system in (a) with initial position q(0)=a and initial momentum p(0)= wb. a and b are real constant.

A ρ。'ntc, p by ferce pro portional to its dis knte fron . If t denotes tre the Punctven) obey s Ne mass m=1 no vesen alae R, at tracted to the origine Where w iss Posit i ue constant ,This ,s know, as the Mumon.lOulleh'F.q order EA. Wrde this Haininic as a system or the crent matiz re s con ding Coe Solve the Intral valve Protten or in (a) with ın,tial pos, ton a(の=a & ntial momentum Co)-w b Here b are se Con s sst A point of mass m 1 moves on a line R, attracted to the origin O by a free proportional to its distance from 0. If t denotes time, the functiont+g(t) obeys Newton's law where w is a positive constant. This is known as the harmonic oscillator equation (a) Let p - q and show that the the harmonic oscillator equation can be written as a system of irst order equations. Write this harmonic oscillator system and the corresponding coefficient matrix A

Answer 1

weu 2nd obtaind two or we dauo wl have n Ui «quatioii become 2 tha

Co Llut sinu co 1(o)a A -a use