Force excitation equation of motion proof

The video tutorial explains how to derive the equations of motion for a spring-mass-dampener system with an external force. It covers the use of Newton's laws to form mathematical expressions and explores particular solutions, including sinusoidal forces. The tutorial also clarifies different types of omega, such as natural and damped frequencies, and demonstrates how to simplify expressions using dampening ratios and natural frequencies.

What is the role of the spring force in a spring mass dampener system?

• It accelerates the mass.

• It resists displacement.

• It increases velocity.

• It acts as an external force.

Which law is used to derive the equations of motion for the spring mass dampener system?

• Ohm's Law

• Newton's Laws

• Coulomb's Law

• Hooke's Law

What is the natural frequency of a system?

• The frequency of the block without damping.

• The frequency of the external force.

• The frequency of the system at rest.

• The frequency of the damped system.

What does the damped natural frequency represent?

• The frequency of the external force

• The frequency of the block with damping

• The frequency of the block without damping

• The frequency of the system at rest

What happens when the force frequency equals the natural frequency?

• The system becomes unstable.

• The system reaches resonance.

• The system stops moving.

• The system's mass increases.

What is the assumed form of the particular solution for the differential equation?

• X = X sin(omega t - phi)

• X = X exp(omega t - phi)

• X = X tan(omega t - phi)

• X = X cos(omega t - phi)

How is the phase angle phi determined in the solution?

• Using the cosine rule

• Using the sine rule

• Using the inverse sine function

• Using the tangent rule

What is the purpose of using trigonometric identities in the solution?

• To eliminate the damping

• To change the frequency

• To complicate the solution

• To simplify the expression

What is the significance of the dampening ratio in the solution?

• It determines the mass of the system.

• It affects the amplitude of the solution.

• It alters the spring constant.

• It changes the external force.

How is the amplitude of the particular solution expressed?

• As a function of mass and damping

• As a function of force and spring constant

• As a function of force and frequency

• As a function of spring constant and damping