\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \tau{\uptau}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\) \(\def \ccw{\circlearrowleft}\) \(\def \cw{\circlearrowright}\)

How Things Move

Why Things Move

Index for
Chapter 8: Fluids

Index for
Chapter 10: Waves

Index for
Chapter 9
Oscillations

1. What Are Oscillations?

oscillation
cycle
period
equilibrium point
restoring force
displacement
alternating current
amplitude

2. Period and Frequency

period
frequency
hertz
\(f=\frac{1}{T}\)

3. Block on a Spring

relaxation length
\(T=2\pi\sqrt{m\over k} \qquad f=\frac1{2\pi}\sqrt{k\over m}\)

4. Pendulum

pendulum

5. Simple Harmonic Motion

simple harmonic motion
initial phase
\(y(t) = A\cos\left(2\pi {t\over T}+\phi_0\right)\)
\(y(t) = A\cos\left(2\pi ft+\phi_0\right)\)

6. History Graphs

history graph

7. Velocity and Acceleration

\(v_{\max} = 2\pi fA \qquad a_{\max} = 4\pi^2f^2A\)

8. Energy

\(E_{tot} = \frac12kA^2\)

9. Damped Oscillation

damped oscillation
underdamped
overdamped
critical damping

10. Forced Oscillation