-Are the functions that describe the acceleration and the displacement of an undamped

harmonic oscillator always having the same form and at the same time having opposite sign?

-Be able to calculate from the resonance frequency the physical parameters of the system for

all sort of harmonic oscillators (mass-spring, pendulum, Helmholtz, LC-circuit); for example:

The gravitation constant is 9.8, the frequency is 1 Hz, what is the length of the pendulum in

meter?

-Be able to calculate the resulting sine wave frequency from the network coefficient “c” with

a given sampling rate? [suggestion: invert the formula with the c=2.cos(γ)]

-Give a formula that relates the resonance frequency of the system to the physical parameters

of the un-damped mass-spring system?

-Give a formula that describes the resonance frequency fo in the physical parameters of a

damped harmonic oscillator (mass-spring system with resistance)?

-Will the resonance frequency go up, go down, or stay constant when the resistance within an

analog harmonic oscillating system is going up?

-Give a formula that describes the exponential damping “p” in the physical parameters of the

harmonic oscillator?

-Be able to calculate the “decay modulus” and the damping factor from a given oscillogram?

-Give an interpretation for the “r” in the system coefficients?

-Give a formula that relates the damping factor “p” to the damping per sample “r”?

-Give a formula that relates the angular frequency “γ” to the resonance frequency “fo” using

also the sampling frequency “fs”?

-Is it above or below the resonance frequency that the harmonic oscillator system will vibrate

with opposite phase in relation to a sinusoidal driving force?

-Give the formula that relates the exponential damping factor “p” to the band-width “B”?

-Give a time-domain and a frequency-domain interpretation of the Q-factor?

-Give a formula that relates the bandwidth to the resonance frequency for a constant-Q

system?

-Indicate the three regimes in the frequency domain where a damped harmonic oscillator is

stiffness-controlled, mass-controlled, resistance-controlled and explain why these terms are

chosen?

-The two filter coefficients for a second-order recursive filter are 1.9897 and –0.987 calculate

the angular frequency “γ” and the damping per sample “r”.

-Will there be a change in resonance frequency with the digital harmonic oscillator when the

damping per sample “r” changes?