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- A three-blade wind turbine used for research is supported on a shaft so that it is free to rotate about O. One technique to determine the centroidal mass moment of inertia of an object is to place a known weight at a known distance from the axis of rotation and to measure the frequency of oscillations after releasing it from rest with a small initial angle. In this case, a weight of Wadd = 50 lb is attached to one of the blades at a distance R = 20 ft from the axis of rotation. Knowing that when the blade with the added weight is displaced slightly from the vertical axis, and the system is found to have a period of 7.6 s, determine the centroidal mass moment of inertia of the three-blade rotor.vibrating body with viscous damping makes 10 complete oscillations per second, and in 50 cycles diminishes to 20 percent. Determine the damped natural frequency, logarithmic decrement and the damping ratio.A 11-lb wheel is mounted on a 2-lb plate whose center is attached to a 1.6 in diameter, 30 in long (G = 11606.22 kips/in^2) steel bar, which is fixed at its other end_ The centroidal polar moment of inertia of the plate is 220 slugs-in^2. The period of torsional oscillation of this assembly is 0.15 s. What is the polar moment of inertia of the wheel?
- A spring, with a 54 lb/in spring constant, is mounted on a vertical wall to support a 64.4 lb mass. At t=0 and an initial velocity of 9 in/sec. to the left, the mass is released from a position 2 inches to the right of the equilibrium position. Determine: a. Angular frequencyThe following vibration system oscillates with a small angle. x = 0.6m, y = 1.8m, k = 18N/m. From the motor: static deflection = 0.2m, forcing frequency = 30 rad/s. If the starting angle from rest is 2 radians (counter-clockwise) and mass A is 10 kilograms, determine: 1. The natural frequency in radians per second. 2. The natural period in second 3. The amplitude of free vibration in meters (reference: neutral position of the spring below), 4. The amplitude of steady-state vibration in meters (reference: neutral position of the spring below) 5. The magnification factor 6. The overall displacement in meters when t= 1 second (reference: neutral position of the spring below).A wheel is mounted on a shaft (G= 80x10^9 N/m^2) of length 3 m and radius 1 cm. The wheel is rotated 5 degrees and is released. The period of oscillation is observed as 2.3s. Determine the mass moment of inertia of the wheel.
- question 2 A mass ! hangs on the end of a cord around a pulley of radius 5 and moment of inertia 6, rotating with an angular velocity ,, as shown in the figure below. The rim of the pulley is attached to a spring (with constant 7). Assume small oscillations so that the spring remains essentially horizontal and neglect friction so that the conservation of energy of the system yields: 1 2 !91 + 1 2 6,1 + 1 2 7;1 − !); = =, ?ℎABA , = 9 5 , = = CDE&/, ; = FG&H'5CA!AE/ IBD! AJ(G'GKBG(! Find the natural circular frequency of the system in terms of !, 5, 7,6, and ).A hockey puck oscillates on a frictionless, horizontal track while attached to a horizontal spring. The puck has mass 0.160 kg and the spring has force constant 6.00 N/m. The maximum speed of the puck during its oscillation is 0.350 m/s. What is the amplitude of the oscillation? What is the total mechanical energy of the oscillation? What is the potential energy of the puck when the displacement of the glider is 0.0300 m? What is the kinetic energy of the puck when the displacement of the glider is 0.0300 m?The complete slide- back and forth motion of a single reciprocating compressor piston completes in a 2-sec period. The volume displacement of the piston though the piston cylinder is 8,902.63 in3. The stiffness of crank is said to be equal to 65.5N/m and the mass of the said piston is at 10kgs. A.)Draw out your conclusion of the vibration found during the motion of the piston through its piston cylinder.
- A body vibrating with viscous damping makes five complete oscillations per second, and in 10 cycles its amplitude diminishes by 1/5 of the orginal value. Determine the logarithmic decrement and the damping ratio.(a) A mass suspended from a helical spring of stiffness s, is displaced by a distance x from its equilibrium position and allowed to vibrate. Show that the motion is simple harmonic. (b) A vertical helical spring having a stiffness of 1540 N/m is clamped at its upper end and carries a mass of 20 kg attached to the lower end. The mass is displaced vertically through a distance of 120 mm and released. Find : 1. Frequency of oscillation ; 2. Maximum velocity reached ; 3. Maximum acceleration; and 4. Maximum value of the inertia force on the mass. (c) A machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out vibrations. There are three springs each of stiffness 10 N/mm and it is found that the amplitude of vibration diminishes from 38.4 mm to 6.4 mm in two complete oscillations. Assuming that the damping force varies as the velocity, determine : 1. the resistance of the dashpot at unit velocity ; 2. the ratio of the frequency of the damped vibration to the…Find the periodic-time (T) of a simple pendulum if its natural frequency (ω_n= 54+12) rad/s and length is (35+12) cm.