Unit 7 Review: Oscillations in AP Physics 1

Introduction

• Topic: Oscillations
• Source: AP Physics 1 Ultimate Review Packet
• Key concepts: Periodic Motion, Simple Harmonic Motion (SHM)

Periodic Motion

• Definition: Motion repeated in equal intervals of time.

Simple Harmonic Motion (SHM)

• Definition: Periodic motion resulting from a restoring force proportional to the displacement from equilibrium.
• Equilibrium Position: Net force and acceleration are zero; object can remain at rest.
• Restoring Force: Directed towards equilibrium.
• Examples:
  • Hands of an analog clock (periodic but not SHM).
  • Ideal mass-spring system (both periodic and SHM).
  • Characteristics of an ideal mass-spring system: Massless, frictionless spring, and surface.

Characteristics of SHM

• Period (T): Time for one full cycle or oscillation.
• Amplitude (A): Maximum distance from equilibrium position.

Mass-Spring System Positions

• Positions numbered as 1, 2, 3.
• Full cycle examples: 1, 2, 3, 2, 1; 2, 3, 2, 1, 2; etc.

Dynamics at Key Positions

1. Position 1:
   • Velocity = 0 (momentarily).
   • Displacement = Amplitude.
   • Maximum force and acceleration (left direction).
2. Position 2 (Equilibrium):
   • Displacement = 0.
   • Force and acceleration = 0.
   • Maximum velocity (left or right).
3. Position 3:
   • Displacement = -Amplitude.
   • Maximum force and acceleration (right direction).
   • Velocity = 0.

Equations and Effects

• Period of Mass-Spring System:
  • [ T = 2\pi \sqrt{\frac{m}{k}} ]
  • Increase mass ⟹ Increase period.
  • Increase spring constant ⟹ Decrease period.
• Simple Pendulum Equation:
  • [ T = 2\pi \sqrt{\frac{L}{g}} ]
  • Increase length ⟹ Increase period.
  • Increase gravitational field ⟹ Decrease period.
• SHM Validity:
  • Small angles (≤ 15 degrees for AP Physics 1).
  • Frequency (f): Number of oscillations per second (Hertz, Hz).
  • Frequency = 1/Period.

Graphs

• Position: Cosine wave.
• Velocity: Negative sine wave.
• Acceleration: Negative cosine wave.

Energy in SHM

• Total Mechanical Energy:
  • Constant in isolated systems.
  • Maximum Kinetic Energy ⟹ Minimum Potential Energy and vice versa.
• Elastic Potential Energy in Mass-Spring System:
  • [ PE = \frac{1}{2} k x^2 ]
  • Total Mechanical Energy = ( \frac{1}{2} k A^2 ).
  • Increase amplitude ⟹ Increase total mechanical energy.
• Maximum Speed:
  • [ v_{max} = A \sqrt{\frac{k}{m}} ]
  • Increase amplitude ⟹ Increase maximum speed._

Conclusion

• Understanding and applying these concepts and equations are crucial for mastering oscillations in AP Physics 1.