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(d^2 i)/(d t^2 ) + 25i = A0 sin (ϖt)

assuming that ϖ^2 ≠ 25, determine the current i in terms of the parameters (ϖ and A0) and the variable t when the initial conditions are

i(0) = di/dt (0) = 0

i really don't have much of an idea what to do here.

so far i have found

L.F ic= Acos(5t)+Bsin(5t)

P.S ip = acos(ϖt) + bsin (ϖt)

ip' = -ϖasin (ϖt) + ϖbcos (ϖt)

ip'' = -2ϖacos (ϖt) - 2ϖbsin (ϖt)

therefore

[-2ϖacos (ϖt) - 2ϖbsin (ϖt)] + [acos(ϖt) + bsin (ϖt)] = A0 sin (ϖt)

any help or further guidance to the work i have done would be much appreciated