April 29, Week 15 Today: Chapter 14, Periodic Motion Homework - PowerPoint PPT Presentation

April 29, Week 15 Today: Chapter 14, Periodic Motion Homework Assignment #11 - Due May 3. Mastering Physics: 7 questions from chapters 13 and 14. Mastering Physics: 13.77 Exams will be graded by Wednesday. Newton’s Gravity April 29, 2013 - p. 1/12

Periodic Motion Periodic Motion or Oscillation - Any repeated motion. Newton’s Gravity April 29, 2013 - p. 2/12

Periodic Motion Periodic Motion or Oscillation - Any repeated motion. Terms: Newton’s Gravity April 29, 2013 - p. 2/12

Periodic Motion Periodic Motion or Oscillation - Any repeated motion. Terms: Cycle - One complete round trip. Newton’s Gravity April 29, 2013 - p. 2/12

Periodic Motion Periodic Motion or Oscillation - Any repeated motion. Terms: Cycle - One complete round trip. Amplitude, A - Maximum displacement from zero. Newton’s Gravity April 29, 2013 - p. 2/12

Periodic Motion Periodic Motion or Oscillation - Any repeated motion. Terms: Cycle - One complete round trip. Amplitude, A - Maximum displacement from zero. Period, T - Time for one cycle. Newton’s Gravity April 29, 2013 - p. 2/12

Periodic Motion Periodic Motion or Oscillation - Any repeated motion. Terms: Cycle - One complete round trip. Amplitude, A - Maximum displacement from zero. Period, T - Time for one cycle. Frequency, f - The number of cycles per time. Newton’s Gravity April 29, 2013 - p. 2/12

Periodic Motion Periodic Motion or Oscillation - Any repeated motion. Terms: Cycle - One complete round trip. Amplitude, A - Maximum displacement from zero. Period, T - Time for one cycle. Frequency, f - The number of cycles per time. f = 1 T Newton’s Gravity April 29, 2013 - p. 2/12

Periodic Motion Periodic Motion or Oscillation - Any repeated motion. Terms: Cycle - One complete round trip. Amplitude, A - Maximum displacement from zero. Period, T - Time for one cycle. Frequency, f - The number of cycles per time. f = 1 Unit: 1 s = Hz (Hertz) T Newton’s Gravity April 29, 2013 - p. 2/12

Simple Harmonic Motion Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. Newton’s Gravity April 29, 2013 - p. 3/12

Simple Harmonic Motion Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. Newton’s Gravity April 29, 2013 - p. 3/12

Simple Harmonic Motion Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. 0 Newton’s Gravity April 29, 2013 - p. 3/12

Simple Harmonic Motion Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. 0 x Newton’s Gravity April 29, 2013 - p. 3/12

Simple Harmonic Motion Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. 0 x − → F el Newton’s Gravity April 29, 2013 - p. 3/12

Simple Harmonic Motion Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � − → F = m − → a 0 x − → F el Newton’s Gravity April 29, 2013 - p. 3/12

Simple Harmonic Motion Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � − → F = m − → a 0 x − F el = ma x − → F el Newton’s Gravity April 29, 2013 - p. 3/12

Simple Harmonic Motion Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � − → F = m − → a 0 x − F el = ma x − → F el F el = kx Newton’s Gravity April 29, 2013 - p. 3/12

Simple Harmonic Motion Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � − → F = m − → a 0 x − F el = ma x − → F el − kx = ma x F el = kx Newton’s Gravity April 29, 2013 - p. 3/12

Simple Harmonic Motion Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � − → F = m − → a 0 x − F el = ma x → − F el − kx = ma x a x = − k mx F el = kx Newton’s Gravity April 29, 2013 - p. 3/12

Simple Harmonic Motion II Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. − kx = ma x 0 x − → F el F el = kx Newton’s Gravity April 29, 2013 - p. 4/12

Simple Harmonic Motion II Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. − kx = ma x 0 x − → F el v x = dx F el = kx dt Newton’s Gravity April 29, 2013 - p. 4/12

Simple Harmonic Motion II Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. − kx = ma x 0 x − → F el a x = dv x dt v x = dx F el = kx dt Newton’s Gravity April 29, 2013 - p. 4/12

Simple Harmonic Motion II Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. − kx = ma x 0 x a x = d 2 x dt 2 − → F el a x = dv x dt v x = dx F el = kx dt Newton’s Gravity April 29, 2013 - p. 4/12

Simple Harmonic Motion III Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. − kx = md 2 x dt 2 0 x a x = d 2 x dt 2 − → F el a x = dv x dt v x = dx F el = kx dt Newton’s Gravity April 29, 2013 - p. 5/12

Simple Harmonic Motion III Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. − kx = md 2 x dt 2 � k 0 x d 2 x � dt 2 = − x m → − F el Differential Equation for SHM F el = kx Newton’s Gravity April 29, 2013 - p. 5/12

Simple Harmonic Motion IV Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � k d 2 x � dt 2 = − x m 0 x − → F el F el = kx Newton’s Gravity April 29, 2013 - p. 6/12

Simple Harmonic Motion IV Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � k d 2 x � dt 2 = − x m 0 x In Calculus: f ′′ = − cf − → F el F el = kx Newton’s Gravity April 29, 2013 - p. 6/12

Simple Harmonic Motion IV Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � k d 2 x � dt 2 = − x m 0 x In Calculus: f ′′ = − cf − → x = A cos ( ωt + φ ) F el F el = kx Newton’s Gravity April 29, 2013 - p. 6/12

Simple Harmonic Motion IV Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � k d 2 x � dt 2 = − x m 0 x In Calculus: f ′′ = − cf → − x = A cos ( ωt + φ ) F el F el = kx Amplitude Newton’s Gravity April 29, 2013 - p. 6/12

Simple Harmonic Motion IV Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � k d 2 x � dt 2 = − x m 0 x In Calculus: f ′′ = − cf → − x = A cos ( ωt + φ ) F el Phase Angle F el = kx Amplitude Newton’s Gravity April 29, 2013 - p. 6/12

Simple Harmonic Motion IV Simple Harmonic Motion (SHM) - The simplest type of periodic motion. Occurs when a mass is connected to a spring with no friction. � k d 2 x � dt 2 = − x m 0 x In Calculus: f ′′ = − cf → − x = A cos ( ωt + φ ) F el Phase Angle Angular frequency, F el = kx ω = 2 πf = 2 π Amplitude T Newton’s Gravity April 29, 2013 - p. 6/12

Amplitude Amplitude - Maximum distance from zero. Newton’s Gravity April 29, 2013 - p. 7/12

Amplitude Amplitude - Maximum distance from zero. x = cos t Newton’s Gravity April 29, 2013 - p. 7/12

Amplitude Amplitude - Maximum distance from zero. x = cos t Newton’s Gravity April 29, 2013 - p. 7/12

Amplitude Amplitude - Maximum distance from zero. x = cos t Newton’s Gravity April 29, 2013 - p. 7/12

Amplitude Amplitude - Maximum distance from zero. 1 x = cos t − 1 Newton’s Gravity April 29, 2013 - p. 7/12

Amplitude Amplitude - Maximum distance from zero. x = A cos t 1 x = cos t − 1 Newton’s Gravity April 29, 2013 - p. 7/12

Amplitude Amplitude - Maximum distance from zero. x = A cos t 1 x = cos t − 1 Newton’s Gravity April 29, 2013 - p. 7/12

Amplitude Amplitude - Maximum distance from zero. x = A cos t 1 x = cos t − 1 Newton’s Gravity April 29, 2013 - p. 7/12

Amplitude Amplitude - Maximum distance from zero. A x = A cos t 1 x = cos t − 1 − A Newton’s Gravity April 29, 2013 - p. 7/12

Phase Angle Phase Angle - φ, Units: rad . Shifts the Cosine to start wherever needed. Newton’s Gravity April 29, 2013 - p. 8/12