Mathematics of Vibration [Part 2: Harmonic Excitation]

The video explores the dynamics of a spring mass damper system, focusing on how a stepper motor induces vibrations at various frequencies. It explains the modeling of the system using differential equations, highlighting the transient and steady state responses. Through simulations, the concept of resonance is demonstrated, showing how amplitude changes with frequency. The video further analyzes phase and amplitude relationships, emphasizing the role of velocity and power in the system's behavior. The tutorial concludes with a brief mention of future topics involving additional masses.

What was observed when the stepper motor was used to incite vibrations at different frequencies?

• Vibrations were only observed at high frequencies.

• No vibrations were observed at any frequency.

• Large vibrations occurred near 2.5 Hertz.

• All frequencies caused the same amplitude of vibration.

What are the two parts of the equation of motion derived from the system model?

• Linear response and non-linear response

• Initial response and final response

• Transient response and steady state response

• Static response and dynamic response

What happens to the amplitude when the system is excited at its natural frequency?

• The amplitude skyrockets.

• The amplitude becomes zero.

• The amplitude remains constant.

• The amplitude decreases.

What is the significance of the steady state amplitude in the system?

• It represents the initial amplitude of the system.

• It is the amplitude at zero frequency.

• It is the long-term amplitude of the vibrating system.

• It is the amplitude at infinite frequency.

How are the force and velocity vectors aligned when the phase is 90 degrees?

• They are perfectly aligned.

• They are in opposite directions.

• They are randomly aligned.

• They are perpendicular to each other.

Why do low and high frequencies result in low amplitudes?

• Because the system is not vibrating.

• Because the system is at resonance.

• Because the force and velocity are well aligned.

• Because the force and velocity are not well aligned.

What does the phase value of 0 degrees indicate about the driving force and displacement?

• They are unrelated.

• They are perfectly in phase.

• They are out of phase.

• They are perpendicular.