The amplitude of vibration of a single degree of freedom spring-mass-damper system is observed to reduce to 15 % of its initial value after 5 cycles. Spring stiffness equals (1500 + 007) N/m and mass equals (7.5 + 007) kg. Determine: The undamped natural frequency; The damped natural frequency; The logarithmic decrement; The damping ratio; and The coefficient of damping.

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A: F= movm = M -mot , 0≤ t ≤ t0k = 7.5 × 106 N/mc = 0.2 × 106 N -s/mm0 = 15 kg/sv = 2000 m/sM =…

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.