Exercise 2.7 A

Difficulty Secondary School High school/other
★ Basic Easy
★★ Demanding Basic
★★★ Demanding
★★★★ Difficult
★★★★★ Very difficult

Determine the damping ratio (constant that describes the strength of the damping force), damping factor, natural frequency, angular frequency of the harmonic oscillator, and the frequency and angular frequency of the damped oscillator.

Answer: Harmonic oscillator
Damping ratio C=1,01
Damping factor δ=0,012592215 rad/s
Natural frequency $f_{0}$=1,146187397Hz
Natural angular frequency $ω_{0}$=7,20170781 rad/s

Damped oscillator
Frequency $f_{1}$=1,146185644Hz
Angular frequency $ω_{1}$=7,201696801 rad/s

Exercise 2.7 B

Difficulty Secondary School High school/other
★ Basic Easy
★★ Demanding Basic
★★★ Demanding
★★★★ Difficult
★★★★★ Very difficult

Compare the measured and calculated resonance frequency of the forced oscillator. Also determine the spring constant k of the spring and viscous damping coefficient. Use the values specified in Exercise 2.7 A.

Answer: Resonance frequency (theoretical) $f_{res}$=1,146Hz
Resonance frequency (experimental) $f_{res}$=1,144Hz
Spring constant k=18,5 N/m
Viscous damping coefficient β=7,963 g/s