Review unit 4.

Below is a checklist of topics covered. Please review all homework problems and comparable textbook problems in this unit.

HW12: Chapter 15 Oscillations

Simple harmonic motion: d²x/dt²= - wx, x=Acos(wt+d).

Equation of motions:

• Mass-spring system: ma= - kx
• Cons of energy: E=K_max=U_max= K+U, K=E sin²q, U=E cos²q, q= wt+d.
• Physical pendulum: I_Pa= - mgdsinq, Parallel axes theorem: I_P = md²+I_cm.
• Small angle approximation: I_Pa= - mgdq.

EOM and description of the solution:

• Damped pendulum: ma= - kx – bv. Q=2pE/DE.
• An oscillator driven by a sinusoidal force. ma+kx+ bv=F₀coswt.
• Resonance occurs when w_driving ~ w₀
• Maximum resonance amplitude: A=(F₀/k) Q.

HW13. Ch16 (waves), Ch17 Sound waves: part I

Traveling waves: y=Acos(kx-wt), v_waves=w/k=l/T. Along a string: v_waves=(F/m)^1/2

Superposition of waves

• Beats: Addition of two oscillations with slightly different frequencies
• Addition of 2 identical waves moving along the same direction with different phase angles: y1=Acos(kx-wt), and y2=Acos(kx-wt + f)
• Standing waves

Sound waves:

• Sound intensity: I= power/area. Point source: I=I₀/(4pr²).
• Sound level: b=10log₁₀ I/I_0. If b₁=10log₁₀ I₁/I₀, b_N=10log₁₀ N + b₁.
• Speed of sound: v=(gP/r)^1/2. g=1.4.
• Standing waves in air columns with open/close ends. The wave speed is v. What are the wavelengths and the frequencies for following two cases:
• Open-open
• Open-close

HW14. Ch17: part II

§ Doppler shifts

§ Mach cone

Ch18: Fluid statics

§ The static rgh pressure: P=rgh=rg(H-y), or P+rgy = const, Bounoulli’s principle in the static case.

§ Gauge pressure = Absolute pressure – 1atm. pressure.

§ Pascal’s law: Hydraulic pressure.

§ Archimedes principle. B=m_liq^displg=r_liqV^displ g.

Fluid-dynamics

§ Continuity equation

§ Bernoulli’s principle

§ Applications:

o OM ex12-14

o See hw14 for more examples.