Periodic Motion and Waves

Question 1

Simple Harmonic Motion

Answer 1

• Vibratory motion is referred to as s__imple harmonic motion (SHM)
  
  • Cyclic process where an object ondergoes a repeated pathway at uniform intervals

Question 2

Period

Frequency

Amplitude

Answer 2

• Period (T) is the time required to complete one full cylce of motion
  
  • time/vibration
• Frequency (f) is the number of vibrations that occur during a specified amount of time
  
  • f = 1/T
  • Hz (s^-1)
• Amplitude (A) is the magnitude of displacment from the object’s equilibirum
  
  • meters

Question 3

Dampened Harmonic Oscillation

Answer 3

• Period remains constant throughout
• Speed decreases along consecutive maxima; therefore so does KE
• Altitude deceases

Question 4

Elastic

Answer 4

• A spring is elastic; it experiences a deformation while being compressed or stretched

Question 5

Hooke’s Law

Answer 5

• The relationship between the force needed to displace the spring and the force constant is known as Hooke’s law
  
  • F = -kx
  • Negative sign indicates that it is a restoring force

Question 6

Potential Energy of Spring

Answer 6

• U_spring = (1/2)kx²

Question 7

Period and Frequency of Spring System

Answer 7

• T_spring = 2π(m/k)^1/2
• f_spring = 1/(2π)(k/m)^1/2

Question 8

Simple Pendulum

Answer 8

• Two forces that act on a simple pendulum
  
  • Tension in the cord
  • Weight (mg) of the object at the end of the cord
• F_restoring = -mgsin(θ)

Question 9

Potential Energy of a Pendulum

Period of a Pendulum

Frequency of Pendulum

Answer 9

• U_pendulum = -mgL(1 - cos(θ))
• T_pendulum = 2π(L/g)^1/2
• f_pendulum = 1/(2π)(g/L)^1/2

Question 10

Transverse and Longitudinal Waves

Answer 10

• A transverse wave causes vibrations perpendicular to the direction of wave propogation (water wave)
• A longitudinal wave causes vibrations parallel to the direction of wave propogation (sound wave)

Question 11

Speed of a Transverse Wave

Answer 11

• v = (T/μ)^1/2
  
  • T = period
  • μ = mass per unit length
• v = λf

Question 12

Beats

Answer 12

• A phenomenon known as a beat occurs when two waves of differnt wavelengths interfere with each other
• f_beat = |f₂ - f₁|

Question 13

Standing Wave Harmonics

Answer 13

• λ_n = 2L/n
• f_n = (nv)/(2L)