Homework:- 1- The amplitude of vibration of an undamped system is measured to be (1 mm). The phase shift from (t = 0) is to be (2 rad) and the frequency is found to be (5 rad/s). Calculate the initial conditions that caused this vibration to occur. Assume the response is of the form x(t) =A sin(wn.t + o).
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- The amplitude of vibration of an undamped system is measured to be 1 mm. The phase shift from t = 0 is measured to be 2 rad and the frequency is found to be 5 Hz. Determine the initial displacementass 4. vib . Give detailed description of at least two methods of vibration control.A machine weighing 300lb is mounted on a supporting system consisting of four springs and four dampers. The vertical deflection of the supporting system under the weight of the machine is measured as 0.75in. The dampers are designed to reduce the amplitudeof vertical vibration to one-sixthof the initial amplitude after two complete cycles of free vibration. Find the following undamped natural frequency,damping ratio, and damped natural frequencyofthesystem.
- When presented as a free response to a 2kg mass system, a static strain test was conducted and a stiffness of 1.5KN/m was given. The first highest amplitude was 9 mm at t1 and the second highest was 1 mm at 12 had an amplitude of 1 mm at t2. Calculate the attenuation factor.What kind of a free vibration with a response of (d^2 x/dt^2) + 6(dx/dt) + 9x = 0. Initial displacement and velocity are 0 and 1 m/s respectively Overdamped Critically damped Undamped UnderdampedThe pointer of the vibration measuring instrument is observed to move between the 0.1 and 0.3 marks on the vertical scale, when subject to a displacement alternating at a frequency of 100 rad/s. What would the excursion be if the forcing frequency were doubled?
- A punching machine requires 1600 ft-lb of energy to punch a certain hole. During the punching operation, the speed of the machine is reduced from 180 rpm to 160 rpm. The weight of the arms and hub is considered to be 10 % of the rim weight, and the mean diameter of the flywheel is 32 inches. a) What is the mean or operating rpm of the flywheel? b) Find the coefficient of fluctuation. c) What is the maximum speed of the flywheel, in fps? d) What is the minimum speed of the rim, in fps? d) Determine the weight of the rim, in lb. e) What is the weight of the flywheel, in lb? f) Determine the weight of the arms and hub, in lb.calculate the damping factorThe amplitude of vibration of an undamped system is measured to be 1 mm. The phase shift from t = 0 is measured to be 2 rad and the frequency is found to be 5 rad/s. Determine the initial displacement. * 3.6 mm/s - 2.1 mm/s - 7.4 mm/s 6.1 mm/s