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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
