Derive the mathematical relation for the energy dissipation in a vibration cycle for a single degree of freedom mass-spring-damper system subject to initial conditions.
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Step 1
The total energy of a mass-spring-damper system is the sum of its kinetic energy and potential energy: E = K + U where K is the kinetic energy and U is the potential energy. The kinetic energy of the system is given by: K = (1/2)mv^2 where m is the mass of Show more…
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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 1509 N/m and mass equals 16.5 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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