1. The problem statement, all variables and given/known data Verify that Ae^(-βt)cos(ωt) is a possible solution to the equation: d^2(x)/dt^2+ϒdx/dt+(ω_0)^2*x = 0 and find β and ω in terms of ϒ and ω_0. 2. Relevant equations N/a, trig identities I suppose. 3. The attempt at a solution I think this is simply a 'plug and chug' type equation, but I'm having alll sorts of difficulty canceling things. I first calculated the first and second derivative of the given possible solution. First derivative = Ae^(-βt)*(-ωsin(ωt))+(-Aβe^(-βt)cos(ωt)) Second derivative = -Ae^(-βt)ω^2cos(ωt)+Aβe^(-βt)ωsin(ωt)+Aβ^2e^(-βt)cos(ωt)+Aβe^(-βt)ωsin(ωt) I then plugged them into their respective spots into the equation and tried to simplify. I factored and divided both sides by Ae^(-βt). I am at: 2βωsin(ωt)+β^2cos(ωt)-ϒ(ωsin(ωt)+βcos(ωt))+(ω_0)^2cos(ωt)-ω^2cos(ωt) = 0 The problem I am having is visualizing how the terms can cancel. How does a term with ϒ cancel with terms with ω and terms with (ω_0)^2 I have to be missing something.