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## Main Question or Discussion Point

confusing title i suspect but didnt know what else to call it.

so i'm considering a spring and mass with the displacment 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 displacment 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