Reading: Ch. 14 in Knight.
Problems: See HW Set here.
- The derivation of the differential equation for oscillatory motion, eqns. 14.32 and 14.45. You should note how that is derived from F = ma, where a = x”, and be able to take two derivatives of x = A cos(ωt + constant) to show how that results in a solution to the equation.
- Note that the small angle approximation in 14.46 just comes from the linear approximation (or Taylor series) for the sine.
- Be sure to think about the relationship between the period T and the frequency f, and also about why we use the angular frequency ω = 2πf.
- Definitely memorize that ω = √(k/m)
- Definitely memorize Hooke’s Law, F = -kx.
- Energy is important, but secondary to the above. Damped oscillations are important, but secondary to everything else… leave damping for the second time you look at the material.
Reading: Ch. 5.1 – 5.3 in HH
- See HW Set here. WileyPlus due Thursday 11:59PM, hand in some Friday 9:30AM.
- The physical meaning of the area under a curve… if the curve is the velocity vs time, then the area under it is… what?
- Section 5.3, The Fundamental Theorem of Calculus, is… very important. Focus on that.
- The most important thing is to start developing a sense of what in integral is.
- HH doesn’t do this as well as I’d like: an integral is really the opposite of a derivative (note the title of Ch 6, the “anti-derivative”), and a definite integral is just the reverse of a derivative with two numbers (the “limits of integration”) plugged in. Every derivative you know how to do, you already know how to reverse… so you’re more than halfway there!
- Integrals are just adding up lots of bits of something. Anytime you have to add up bits, use an integral. An obvious time to add up bits might be if you are driving — you go a distance x = v * dt in every bit of time dt. But what if your speed keeps changing? Then v = v(t), and the distance you go in any bit of time dt will vary depending on your speed at that moment, so dx = v(t) * dt. And you need to add up all the dx’s to see how far you went… which is the same as adding up all the v(t) * dt’s … which is the “integral over v(t) dt”.
- If the above didn’t make sense, read HH, then read it again. The most critical thing is to understand WHAT you are doing. HOW to do it is secondary.
- The reading for Chemistry in week 12 is Chapter 13 – Chemical Equilibrium. The Reading Response for this week is available here. The Reading Response is due Monday, Jan. 11th at 8 pm.
- Problem Set: Chapter 13 #10, 16, 21, 24, 30, 37, 41, 53, 54, 67, 68, 70, 77, 78, 81, 106
- Chemistry Lab for Week 12 is available here. The Prelab assignment should be completed in your chemistry notebook and presented for a check at the beginning of lab. Note: Physics+Calculus only students do not need to attend the lab this week.