Consider the statement E = E En, with E the energy of the system and E, x wA? the energy in the nth mode of ocillation, which has angular frequency Wn and amplitude An- It was true in the linear case. Which of the statements below are true when it comes to non-linear oscillations? O The expression still works, what changes is the independence of the modes. It is still true in the non-linear case. O The only difference is that the amplitude in each mode depends on the energies in the other modes. The expression still works. We just need to take into account the non-linear interactions between modes in the system to compute the energy in each mode at the beginning, and then we have solved the problem for all times. It isn't valid in the non-linear case anymore Lyapunov exponents. (check all that apply) . are a way to measure collapse onto cycle attractors O . are hard to measure precisely, which is OK, we mostly need to know their sign. O . are a way to express sensitivity to initial conditions /hat is the best graph to have a bird's eye view of if and under what conditions a system undergoes haos? O Phase plot Time series

Consider the statement E = E En, with E the energy of the system and E, x wA? the energy in the nth mode of ocillation, which has angular frequency Wn and amplitude An- It was true in the linear case. Which of the statements below are true when it comes to non-linear oscillations? O The expression still works, what changes is the independence of the modes. It is still true in the non-linear case. O The only difference is that the amplitude in each mode depends on the energies in the other modes. The expression still works. We just need to take into account the non-linear interactions between modes in the system to compute the energy in each mode at the beginning, and then we have solved the problem for all times. It isn't valid in the non-linear case anymore Lyapunov exponents. (check all that apply) . are a way to measure collapse onto cycle attractors O . are hard to measure precisely, which is OK, we mostly need to know their sign. O . are a way to express sensitivity to initial conditions /hat is the best graph to have a bird's eye view of if and under what conditions a system undergoes haos? O Phase plot Time series