Given a simple passive RC low-pass filter, as sketched below. R To do: Prove that this circuit

Given a simple passive RC low-pass filter, as sketched below.

  

Transcribed Image Text:

R To do: Prove that this circuit operates as a first-order system. Question 2: Second-order spring-mass-damper system Given: The most common example of a second-order system is that of a spring, mass, and damper. An idealized schematic is sketched to the right. The spring has spring constant k, and the damper has damping constant c The mass is m, and the forcing function is some force F(1). Output y is defined as the vertical position of the top of the mass. The gravity force may act in any direction, but is not considered as a separate force here; the effect of gravity is included in the forcing function. Spring Damper (c) Mass (m) F To do: Prove that this system operates as a second-order system. R To do: Prove that this circuit operates as a first-order system. Question 2: Second-order spring-mass-damper system Given: The most common example of a second-order system is that of a spring, mass, and damper. An idealized schematic is sketched to the right. The spring has spring constant k, and the damper has damping constant c The mass is m, and the forcing function is some force F(1). Output y is defined as the vertical position of the top of the mass. The gravity force may act in any direction, but is not considered as a separate force here; the effect of gravity is included in the forcing function. Spring Damper (c) Mass (m) F To do: Prove that this system operates as a second-order system.