1. 15.1 Motion of an Object Attached to a Spring 15.1 Hooke’s law 15.2

2. 15.2 The Particle in Simple Harmonic Motion 15.3 15.4 15.5 15.6 Position versus time for an x(t) = A cos (  t +  object in simple harmonic motion 15.7

3. 15.2 The Particle in Simple Harmonic Motion, cont. 15.8 15.9 15.10 15.11 15.12 15.13 Period

4. 15.2 The Particle in Simple Harmonic Motion, cont. 15.14 Frequency 15.15 Velocity of an object in simple harmonic motion 15.16 Acceleration of an object in simple harmonic motion 15.17 Maximum magnitudes of velocity and acceleration in simple harmonic motion 15.18

5. 15.3 Energy of the Simple Harmonic Oscillator 15.19 Kinetic energy of a simple K = ½ mv 2 = ½ m  2 A 2 sin 2 (  t +  ) harmonic oscillator 15.20 Potential energy of a U = ½ kx 2 = ½ kA 2 cos 2 (  t +  ) simple harmonic oscillator 15.21 Total energy of a simple E = ½ kA 2 harmonic oscillator 15.22 Velocity as a function of position for a simple harmonic oscillator

6. 15.4 Comparing Simple Harmonic Motion with Uniform Circular Motion 15.23 x(t) = A cos (  t +  )

7. 15.5 The Pendulum 15.24 15.25 15.26 Period of a simple pendulum 15.27 15.28 Period of a physical pendulum

8. 15.5 The Pendulum, cont. 15.29 15.30 Period of a torsional pendulum

9. 15.6 Damped Oscillations 15.31 15.32 15.33

10. 15.7 Forced Oscillations 15.34 15.35 15.36 Amplitude of a driven oscillator