For a single degree of freedom spring-mass-damper system, the free vibration response shown in the Fig. P2.10a
Question:
For a single degree of freedom spring-mass-damper system, the free vibration response shown in the Fig. P2.10a was obtained due to an initial displacement with no initial velocity.
Fig. P2.10a Free vibration response for a single degree of freedom spring-mass-damper system
Fig. P2.10b First few cycles of free vibration response for a single degree of freedom spring-mass-damper system
(a) Determine the damping ratio using the logarithmic decrement. Figure P2.10b, which shows just the first few cycles of oscillation, is provided to aid in this calculation. (b) What was the initial displacement for this system? (c) Determine the period of oscillation and corresponding damped natural frequency (in \(\mathrm{Hz}\) ). (d) If the system mass is \(1 \mathrm{~kg}\), determine the spring constant (in \(\mathrm{N} / \mathrm{m}\) ).
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