Also why I start by evaluating the damping factor after n periods and setting it equal to 1/e?Damped oscillation frequency refers to the rate at which a damped harmonic oscillator completes one cycle of oscillation.
The formula for calculating damped oscillation frequency is 1/(2π) * √(k/m), where k is the spring constant and m is the mass of the oscillating object.
The constant 8π² in the formula is derived from the relationship between the angular frequency (ω) and the frequency (f) of the oscillation, where ω = 2πf. This results in the formula being written as 1/(2π) * √(k/m) = 1/√(4π²) * √(k/m) = 1/(2π) * √(k/m) * √(4π²) = 1/(2π) * √(4π²k/m) = 1/(2π) * √(8π²k/m) = 1/(2π) * √(8π²k/m) = 1/√(8π²) * √(k/m) = 1/√(8π²) * √(k/m) = 1/√(8π²) * √(k/m) = 1/(8π²) * √(k/m) = 1-8π²n²-1 where n represents the number of oscillations.
Damping decreases the amplitude of the oscillation over time, which also decreases the oscillation frequency. This is because the energy of the system is dissipated through the damping process.
The factors that can influence damped oscillation frequency include the mass and stiffness of the oscillating object, the amount of damping present, and external forces acting on the system.