- #1
Trying2Learn
- 373
- 57
- TL;DR Summary
- Why must there be two solutions
Consider the second order linear differential equation that describes vibration:
Mass, damping, stifffness and free vibration
If the roots of the characteristic equation are repeated, we have one solution and we must search for a second. We assume it by taking the first solution and multiplying it by time.
Why?
I mean: I get that it works, but all the textbooks say that we MUST search for a second solution.
Now, I know we can do that because we have two initial conditions and a second order equation.
But can someone explain why the books say "we MUST search for another solution. For it seems to me, right now, a case of a hammer in search of a nail. How does one justify a search for a second solution?
Mass, damping, stifffness and free vibration
If the roots of the characteristic equation are repeated, we have one solution and we must search for a second. We assume it by taking the first solution and multiplying it by time.
Why?
I mean: I get that it works, but all the textbooks say that we MUST search for a second solution.
Now, I know we can do that because we have two initial conditions and a second order equation.
But can someone explain why the books say "we MUST search for another solution. For it seems to me, right now, a case of a hammer in search of a nail. How does one justify a search for a second solution?