Homework due date?

• The last homework is due Nov. 29, while the final exam will be one week after it. An argument for moving the due date to Dec. 1, based on the availability of the TA discussion sections has been put forward.
  Note that there won't be any more homework (or quiz). But there will be many pre-final review problems to work on. There will be special and tough (2 or 3 TBD) pre-final review problems that will carry big pay-outs if you solve them and submit correct solutions.

  1. Nov. 29 (Tuesday) seems fine.
  2. I like Dec. 1 (Thursday) better.

B was the majority choice, and so the new date will be Dec. 1.

Normal modes

• One of the following statements is incorrect. Which one?
  1. A normal mode is an eigenstate corresponding to a certain normal mode frequency.
  2. Any actual vibration that happens in a coupled oscillator system must be a normal mode.
  3. In a normal mode, all masses move at the same frequency.
  4. Normal modes are like basis states with which any other physically possible state can be built on by linear combination.

B: any actual motion is a linear combination of normal mode motions.

Normal modes

• How many normal modes does a H$_2$O molecule have?

  1. Three.
  2. Six.
  3. Nine.
  4. Twelve.

C: because there are 9 degrees of freedom in total. Note that normal modes include translational and vibrational modes.

Normal modes

• Consider a ring of atoms, where each atom can move only tangentially. There are a million atoms. How many normal modes exist?
  1. One million.
  2. Three millions.
  3. Hard to say before knowing what those atoms are.
  4. Hard to say before knowing how atoms interact.

A: because there are one million degrees of freedom. No matter how complicated the interactions are! No matter what those atoms actually are!

Normal modes

• How many normal modes does a SiC crystal with a billion molecules have?
  1. One billion.
  2. Two billions.
  3. Three billions.
  4. Six billions.

D: because there are two billion atoms and each atom (Si or C) has 3 degrees of freedom.

Normal modes

• Which of the following has the best value (as in the most bang for the buck) when we figure out normal modes for a given problem?

  1. Newtonian formalism -- solve the EOMs.

  2. Lagrangian formalism -- diagonalize A and M.

  3. Know or guess what normal modes should be based on the separation of the CM motion and the internal motion and any other arguments based on the reflection symmetry etc.

C: one can often expect, and should expect, the answers for many normal mode problems.