-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?
. I can expect questions like:
