Can you draw and describe the response to a step input of a second order system that has a damping coefficient of 0 (under-damped)?

Zero Damping
(Damping Coefficient (ζ) = 0)
  • A theoretical situation in which the system oscillates in response to a step change in the input value and the amplitude of the oscillations does not diminish with time;
  • The system is un-damped because the output value continues to oscillate around the baseline after the input value has changed
  • The amplitude of these oscillations would remain constant, as shown, if no energy was lost to the surroundings. This situation is, therefore, theoretical as energy is inevitably lost, even in optimal conditions such as a vacuum