Question: solving a differential eqn with initial condition plus another condition (under-damped)

Hi,

I am given the differential eqn : 4x'' +3x'+kx=0  with initial conditions  x(0)=0 and x'(0)=1

then I'm asked to:

display a Hooke's constant k>0 such that the solution x(t) is under-damped. Check that    x(t)=0  for infinitely many t>0. Display the exact solution x(t) obrained by maple methods.

On paper I know exactly how to find k such that this system is under damped:  9-16k<0. But how can I make maple understand that. As a result of such a k>9/16 I get complex roots for the characteristic eqn. But again I can do all that on paper.

And then it is asking to check that x(t)=0 for infinitely many t>0. how should i check that? by just visaully inspecting the plot of  the solution to the eqn ( while k>9/16 , an underdamped system)

Thank you guys a lot in advance

Vince