Hey guys, here is the exact question and I have no idea how to explain it (dont worry no calculation involved, I least I dont think). Can anybody explain this to me?
You are given a forced damped oscillator coming from
y''[t] + b*y'[t] + c*y[t] = f[t]
with given starter data
y[0] = p
and
y'[0] = q
(and with
b > 0
and
c > 0
),
Does the steady state (long term, global scale) behavior of this oscillator depend in any way on the specific values of the starting data?
How do you know for sure?
Any help is greatly appreciated!
Derg
PS This is from the exponential DiffEq section
You are given a forced damped oscillator coming from
y''[t] + b*y'[t] + c*y[t] = f[t]
with given starter data
y[0] = p
and
y'[0] = q
(and with
b > 0
and
c > 0
),
Does the steady state (long term, global scale) behavior of this oscillator depend in any way on the specific values of the starting data?
How do you know for sure?
Any help is greatly appreciated!
Derg
PS This is from the exponential DiffEq section
-
under your conditions the steady state will depend only on the forcing function
since the characteristic roots [ - b ± √ ( b² - 4 c ) ] / 2 will always have real part < 0
since the characteristic roots [ - b ± √ ( b² - 4 c ) ] / 2 will always have real part < 0