Below are the graphs of 6 different solutions to mx cx kx

Below are the graphs of 6 different solutions to mx\" + cx\' + kx = F₀cos(wt), x(0) = x₀, x\'(0) = x₁ in red.

(a) For each graph you need to Identify if the graph in red is undamped, underdamped, overdamped, unforced, forced (beats), forced (resonance)?

(b) Using what you determined in part (a), find the initial value problems for which the red graph is the graph of the solution.

Solution

1. Undamped : system oscillates at its natural resonant frequency without experiencing decay of its amplitude.

3. Overdamped : system returns to its equilibrium without oscillating.

4 underdamped : system oscillates with amplitude gradually decreasing to zero

5. Forced( beats)

6. Forced( resonance)