- #1
phlegmy
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confusing title i suspect but didnt know what else to call it.
so I'm considering a spring and mass with the displacement of the mass being x and the stiffness of the spring being k
force on the spring = -k*x =m*a
or rearranged etc
d2x/dt2 + (k/m)*x = 0 .........[1]
then i assume a soln of the form e^(at)
and find a= i*(k/m)^.5 [then let sqrt(k/m)= w)
so i get x= e^(i*w*t)
which using the euler identity gives
x= cos(wt)+i*sin(wt)
great so i managed to show that the thing will move sinusoidly
but what about that i*sin(wt) term
if i ignore it, and let x=cos(wt) this still satisfies [1] above
so am i justified in ignoring it? or does it have some physical significance?
or is it something that just gets "thrown up" as a result of me assuming a soln of the form e^at ?
and more generally
if i find a soln to a diff eqn, and find that by dropping some terms in the soln that it still satifies the eqn am i still justified in doing that?
thanks jim
so I'm considering a spring and mass with the displacement of the mass being x and the stiffness of the spring being k
force on the spring = -k*x =m*a
or rearranged etc
d2x/dt2 + (k/m)*x = 0 .........[1]
then i assume a soln of the form e^(at)
and find a= i*(k/m)^.5 [then let sqrt(k/m)= w)
so i get x= e^(i*w*t)
which using the euler identity gives
x= cos(wt)+i*sin(wt)
great so i managed to show that the thing will move sinusoidly
but what about that i*sin(wt) term
if i ignore it, and let x=cos(wt) this still satisfies [1] above
so am i justified in ignoring it? or does it have some physical significance?
or is it something that just gets "thrown up" as a result of me assuming a soln of the form e^at ?
and more generally
if i find a soln to a diff eqn, and find that by dropping some terms in the soln that it still satifies the eqn am i still justified in doing that?
thanks jim