Question

given that H=1/2mpx^2 + 1/x mw^2x^2

given that m is the effective mass of the oscillator and v is the frequency and w is the angular frequency defined by w=2piv.

given that (A+) = 2m^(-1/2)(px+1mwx) and (A-) = 2m^(-1.2)(px-imwx)

(a) show that (A+)(A-) = H-1/2hv and (A-)(A+)=H+1/2hv

(b) show that [(A+),(A-)]=-hv anbd that [H,A+]=hvA+ and [H,A-]=-hvA-

Answer #1

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Consider the driven damped harmonic oscillator
m(d^2x/dt^2)+b(dx/dt)+kx = F(t)
with driving force F(t) = FoSin(wt).
Consider the overdamped case
(b/2m)^2 < k/m
a. Find the steady state solution.
b. Find the solution with initial conditions x(0)=0,
x'(0)=0.
c. Use a plotting program to plot your solution for
m=1, k=0.1, b=1, Fo=0.25, and w=0.5.

the
equation of mass connected to a spring is given by w^2=k/m and
d^2x/d^2t = -w^2 x
m= 0.2 kg k=5
x(0)=-0.05
x(0.628)=0.05
with step 0.157
by using FORWARD finite difference method solve this ODE

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For the function w=f(x,y) , x=g(u,v) , and
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gu(2,3)=-5,
gv(2,3)=-1 ,
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