12-5 Simple pendulum (p307):

O  l T mg 12-5 Simple pendulum (p307): Restoring force: Comparing to SHM

28-5 Electromagnetic Oscillation (P650) 1. Oscillation circuit Inertial element of current: L L─ C circuit Restoring element of voltage: C Qualitative explanation Electric energy in C Magnetic energy in L Quantitative analysis: emf of self-induction on L= Voltage cross C Since Comparing to q is a SHQ.

2. Discussion: ① Since q is a SHQ, I is a SHQ. I is ahead of q for phase of /2. ③ U is a SHQ. U and q are in phase. Electric energy : ④ Magnetic energy: Total energy: (Conserved）

# Superposition of Oscillations x = x1+ x2 x=Acos( t+) That is, 1. Superposition of Two SHMs in Same Direction with Same Frequency(二同向、同频简谐运动合成): x1=A1cos( t+ 1) x2=A2cos( t+ 2) The resultant oscillation is also a SHM in Same Direction with Same Frequency.

① If f f2 f1 The resultant oscillation is related to the phase difference f2-f1 . Discussion: 1). Two special cases: =A1+A2 —–When the two SHMs are in phase, the resultantamplitude reaches its maximum.

2).In general cases:, ② If A=|A1-A2| —–When the two SHMs are out of phase, the resultantamplitude reaches itsminimum. If A1=A2, then A=0 ! 3). The phase difference of two SHMs plays an important role in the resultant oscillation ! 4). In similar way, we may get the results for the superposition of multi-oscillations .

2. Superposition of N SHMs in Same Direction with Same Amplitude,Same Frequency and SameAdjacent Phase Difference(N同向、同幅、同频、同相邻位相差谐振动合成): N C C b N C R Nb 1 R a A O 1 0 O

Example: x=? Method1: 2 x12 and x3:

Method 2. 3 SHMs in Same Direction with Same Amplitude,Same Frequency and SameAdjacentPhase Difference Method 3: Rotating Vector:

Questions (思考题） • P316 7; P316 11; P316 14 • Problems (练习题） • P320 46; P322 76; P323 85

12-5 Simple pendulum (p307):