Phase Angles and Motion Equations

The video tutorial covers solving simultaneous equations derived from displacement and velocity equations in simple harmonic motion. It begins with an introduction to the equations, followed by substituting t=0 to simplify them. The instructor then demonstrates solving these equations using trigonometric identities and determining the value of alpha. The session concludes with a summary of part A and a brief introduction to part B, encouraging students to apply the learned concepts.

What is the initial condition set for the displacement equation?

• t = 1

• t = 0

• t = 2

• t = -1

How do we simplify the second equation to make it easier to solve?

• Multiply both sides by 6

• Divide both sides by -6

• Subtract 6 from both sides

• Add 6 to both sides

What is the purpose of using simultaneous equations in this context?

• To find the value of t

• To solve for displacement

• To determine the values of a and alpha

• To calculate the velocity

What alternative method is suggested for solving the equations?

• Using a graph

• Using a computer program

• Using auxiliary angles

• Using a calculator

What is the value of the amplitude 'a' derived from the equations?

• 6

• 5

• 4

• 3

Why is the phase angle alpha considered to be acute?

• Because it is in the first quadrant

• Because it is in the second quadrant

• Because it is in the fourth quadrant

• Because it is in the third quadrant

Which quadrant is alpha located in based on the equations?

• First and fourth

• First and second

• Second and third

• Third and fourth

What is the final form of the equation of motion?

• x = 5 sin(6t + 0.9273)

• x = 5 cos(6t + 0.9273)

• x = 4 sin(6t + 0.9273)

• x = 4 cos(6t + 0.9273)

What is the significance of choosing cosine over sine in the final equation?

• It reduces the phase shift

• It makes the equation more complex

• It increases the phase shift

• It has no significance

What is the next step after determining the equation of motion?

• Determine the next time period

• Solve for the next phase angle

• Find the next velocity

• Calculate the next displacement