Blackboard Collaborate: Quick Start Guide

Guía de inicio rápido para Blackboard Collaborate

• This guide provides a general overview of the Collaborate interface.
• It explains how to navigate the system.
• It also tells you where to find further assistance.

Menu

• The menu is located in the top-left corner.
• It contains links to:
  • A guided tour
  • Blackboard Collaborate help
  • A problem report form
  • Information about Blackboard Collaborate

Session Toolbar

• The session toolbar is located at the bottom.
• Features include:
  • Audio and video sharing
  • Raise hand function
  • Connection status

Collaborate Panel

• The Collaborate Panel is located on the right.
• Features include:
  • Chatting with all or only moderators
  • Viewing session attendees
  • Sharing content
  • Managing session settings

Accessibility

• Blackboard Collaborate is committed to accessibility.
• Product documentation adheres to Web Content Accessibility Guidelines (WCAG) 2.1 Level AA.
• Accessibility is an ongoing effort during software design and development.

Transverse Standing Waves

• These waves occur when a string is stretched between fixed points and vibrated.

Relationships

• Antinodes: Points of maximum displacement.
• Nodes: Points of zero displacement.
• The spacing between successive nodes/antinodes equals half a wavelength ($\frac{\lambda}{2}$).
• For a string of length $L$ fixed at both ends, standing waves have wavelengths $\lambda_n = \frac{2L}{n}$, where $n = 1, 2, 3,...$
• Possible frequencies are $f_n = \frac{v}{\lambda_n} = n\frac{v}{2L}$.
• Wave speed on a string is $v = \sqrt{\frac{F}{\mu}}$, where $F$ denotes tension and $\mu$ denotes linear density (mass per unit length).
• Frequencies of normal modes are $f_n = \frac{n}{2L}\sqrt{\frac{F}{\mu}}$, where $n = 1, 2, 3,...$
• The fundamental frequency or first harmonic is the lowest frequency $f_1$.
• Overtones refer to other frequencies.
• The $n^{th}$ harmonic is represented by the frequency $f_n$.

First Harmonic (Fundamental)

• $\lambda_1 = 2L$
• $f_1 = \frac{1}{2L}\sqrt{\frac{F}{\mu}}$

Second Harmonic (First Overtone)

• $\lambda_2 = L$
• $f_2 = \frac{1}{L}\sqrt{\frac{F}{\mu}} = 2f_1$

Third Harmonic (Second Overtone)

• $\lambda_3 = \frac{2L}{3}$
• $f_3 = \frac{3}{2L}\sqrt{\frac{F}{\mu}} = 3f_1$

Fourth Harmonic (Third Overtone)

• $\lambda_4 = \frac{L}{2}$
• $f_4 = \frac{2}{L}\sqrt{\frac{F}{\mu}} = 4f_1$

Statics

Introduction

• Mechanics studies how physical bodies behave under forces/displacements and their effects.

Rigid-Body Mechanics

• Assumes bodies do not deform:
  • Statics: considers bodies at rest/equilibrium.
  • Dynamics: considers bodies in motion.
• Deformable-Body Mechanics: Considers deformation under forces.
• Fluid Mechanics: Studies fluid behavior

Fundamental Concepts

• Space: Geometric region occupied by bodies.
• Time: Measures the sequence of events.
• Mass: Measures the amount of matter in a body.
• Force: Action that tends to cause acceleration.

Newton's Laws of Motion

1. First Law (Inertia): A body stays at rest/motion unless acted upon by net force.
2. Second Law: Net force equals mass times acceleration: $\sum \mathbf{F} = m\mathbf{a}$.
3. Third Law (Action-Reaction): Every action has an equal, opposite reaction.

Units of Measurement

• SI Units:
  • Length: meter (m)
  • Mass: kilogram (kg)
  • Time: second (s)
  • Force: Newton (N), where $1 N = 1 kg \cdot m/s^2$
• US Customary Units:
  • Length: foot (ft)
  • Mass: slug
  • Time: second (s)
  • Force: pound (lb), where $1 lb = 1 slug \cdot ft/s^2$

Scalars and Vectors

• Scalar: Quantity with only magnitude (e.g., mass, time).
• Vector: Quantity with magnitude and direction (e.g., force, velocity).

Vector Operations

• Addition: Use parallelogram/triangle rule.
• Subtraction: $\mathbf{A} - \mathbf{B} = \mathbf{A} + (-\mathbf{B})$.
• Scalar Multiplication: Changes magnitude, not direction, unless scalar is negative.
• Unit Vector: Vector with magnitude of 1: $\hat{\mathbf{u}} = \frac{\mathbf{A}}{|\mathbf{A}|}$.

Coordinate systems

• Cartesian Coordinates: Point defined by (x, y, z).
  • Unit vectors: $\mathbf{i}, \mathbf{j}, \mathbf{k}$ along x, y, z axes.
• Vector Representation: $\mathbf{A} = A_x \mathbf{i} + A_y \mathbf{j} + A_z \mathbf{k}$.
• Magnitude: $|\mathbf{A}| = \sqrt{A_x^2 + A_y^2 + A_z^2}$.
• Direction Cosines:
  • $\cos \alpha = \frac{A_x}{|\mathbf{A}|}$, $\cos \beta = \frac{A_y}{|\mathbf{A}|}$, $\cos \gamma = \frac{A_z}{|\mathbf{A}|}$.
• Dot Product: $\mathbf{A} \cdot \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \cos \theta = A_x B_x + A_y B_y + A_z B_z$ (where $\theta$ is the angle between A and B).
• Cross Product: $\mathbf{A} \times \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \sin \theta \mathbf{n}$ (where $\mathbf{n}$ is a unit vector perpendicular to both $\mathbf{A}$ and $\mathbf{B}$). $$ \mathbf{A} \times \mathbf{B} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \ A_x & A_y & A_z \ B_x & B_y & B_z \end{vmatrix} = (A_y B_z - A_z B_y)\mathbf{i} - (A_x B_z - A_z B_x)\mathbf{j} + (A_x B_y - A_y B_x)\mathbf{k} $$

A quick guide to the Blackboard Collaborate interface. Learn how to navigate the system and where to find help. Covers the menu, session toolbar, collaborate panel and accessibility.