Simple Harmonic Motion and The Spring Mass System

SHM & Energy Conservation

Form of motion where a restoring force pulls an object back toward equilibrium

Follows a sinusoidal motion (displacement over time can be described by sine and cosine)

Energy Conservation

Total mechanical energy (kinetic + potential) remains constant

At max displacement: Kinetic energy = 0, potential energy = max

At equilibrium: KE = max, PE = 0

Pendulum

Restoring force is gravity pulling it back toward the center

Velocity at bottom calculated using Newton’s Laws

Spring Mass System

Restoring force follows Hooke’s Law: F= -kX (force proportional to displacement)

Velocity at equilibrium is at its highest

Better analogy for sound wave propogation

Conditions for Sound Wave Propagation

Both the source and medium must have mass and elasticity for sound waves to travel

Amplitude

Maximum Displacement

Frequency

How many cycles per second (Hz)

Period

Time to complete one cycle (s)

Wavelength

Distance between two peaks (m)

Phase

Positions of the wave at a specific time

In Phase waves

Reach equilibrium at same time

Out of phase waves

Do not reach equilibrium at same time, affecting sound interference

Phase Shifts

Cause a wave to move forward or backward in time

Formula for SHM

Asin(2πft+ϕ)

Describes oscillatory motion

A =1

F = 100 Hz

Hooke’s Law

States that the force exerted by a spring is proportional to its displacement from the equilibrium position, as long as elastic limit is not exceeded

Equation: F = -kx

F = Restoring force exerted by spring

k = spring constant

x = displacement from equilibrium position

Negative sign indicates force is always opposite to direction of displacement