Oscillations and Simple Harmonic Motion

Hooke's Law and Restoring Force

Simple harmonic motion (SHM) describes the oscillatory motion of systems where the restoring force is proportional to displacement and directed toward equilibrium.

• Hooke's Law: The restoring force in a spring is given by:

• k: Spring constant (N/m)

• x: Displacement from equilibrium (m)

Position as a Function of Time

The displacement of an object in SHM can be described by:

• A: Amplitude (maximum displacement)

• \omega: Angular frequency (rad/s)

• \varphi: Phase constant (rad)

Velocity and Acceleration in SHM

• Velocity:

• Acceleration:

• Relationship:

Energy in SHM

• Kinetic Energy (KE):

• Potential Energy (PE):

• Total Mechanical Energy:

Period and Frequency

• Period (T):

• Frequency (f):

• Angular Frequency:

Waves and Sound

Wave Speed

• Speed of Sound in Air: (in m/s, where is temperature in °C)

• Speed of Light in Vacuum: m/s

Wave Relationships

• Wave Speed:

• Frequency and Wavelength in Different Media: and

Doppler Effect

• Observed Frequency (Doppler Effect):

• f': Observed frequency

• f_s: Source frequency

• v: Speed of sound

• v_L: Speed of listener (positive if moving toward source)

• v_s: Speed of source (positive if moving away from listener)

Beat Frequency

• Beat Frequency:

Wave Optics

Snell's Law (Refraction)

• Snell's Law:

• n: Index of refraction

• \theta: Angle with respect to the normal

Thin Film Interference

• Constructive Interference:

• Destructive Interference:

• t: Thickness of film

• \lambda_f: Wavelength in film

• m: Integer (order of interference)

Geometric Optics

Magnification and Lens Equations

• Magnification (M):

• Lens Equation:

• Total Magnification (multiple lenses):

Summary Table: Key Formulas

Example: If a sound wave travels in air at 20°C, its speed is m/s.

Example: For a spring with N/m and m, the total energy is J.

Additional info: Some formulas were expanded with definitions and context for clarity and completeness.