Civil meant Using a mass of 50 kg and a spring with a rigidity of 4 x 40 N/m, a vibrating system is viscously dampened. Two successive amplitudes have a 20:18 ratio. Find the undamped system's natural frequency. Calculate the damped natural frequency and damping ratio as well.

Q3. An aluminium-alloy cylinder of internal diameter 10.000cm and wall thickness 0.50cm is shrunk onto a steel cylinder of external diameter 10.004cm and wall Thickness 0.50cm. If the values of Young's modulus for the alloy and the steel are 70 GN/m² and 200 GN/m", respectively, estimate the circumferential stresses in the cylinders and the radial pressure between the cylinders. SPARK4

Question 6 (a)-Determine the natural frequency of vibration and mode shape corresponding to first and last mode of vibration for the shear building shown in following figure. N=2 ms=(IN) ksec/in kç= (200N) k/in m₁= (2N) ksec²/in k= (400N) k/in ms=(3N) ksec/in kj= (600N) k/in m₂= (4N) ksec²/in k₂= (800N) k/in m₁= (5N) ksec²/in k₁= (1000N) k/in

A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of stiffness k. Considering z as the displacement of the system at any time t, the equation of motion for the free vibration of the system is mž + kz = 0. The natural frequency of the system is