t Calculate the three lowest natural frequencies of a solid 20 cm radius steel shaft (G=80* 10' N/m²³, p = 7500 kg/m³) with a length of 1.5 m that is fixed at one end and free at its other end. Fixed free
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- A wire of length L₁ = 30 cm has one end fixed and the other end welded to another wire, whose linear density of mass is 4 times smaller. The second wire passes through a pulley and a mass of 10 kg is suspended by its other end. The distance L₂ between the weld point and the pulley is 80 cm. A stationary wave is produced in the composite wire, whose ends at the left wall and the pulley remain fixed. If the frequency is as low as possible and there is one node (node) at the solder point, what is the number of nodes (nodes) of this stationary wave, including the nodes (nodes) at the left wall and the pulley? a. 3b. 4c. 5d. 6e. 7f. 8g. 9h. 10a. 11j. 12k. 13l. 14m. 15A wire of length L1=30cm has a fixed end and the other end is welded to another wire, whose linear mass density is 4 times smaller. The second wire passes over a pulley and a mass of 10kg is suspended from its other end.The distance L2 between the welding point and the pulley is 80 cm. A standing wave is produced in the composite wire, whose ends on the left wall and on the pulley remain fixed.If the frequency is as low as possible and there is a node at the weld spot, what is the number of nodes in this standing wave, including nodes on the left wall and on the pulley?a)3b)4c)5d)6e)7f)8g)9h)10i)11j)12k)13l)14m)15Does an automobile radio antenna vibrate in resonance dueto vortex shedding? Consider an antenna of length L anddiameter D . According to beam vibration theory [, the fi rst mode natural frequency of a solidcircular cantilever beam is ω n = 3.516[ EI /( ρ AL 4 )] 1/2 ,where E is the modulus of elasticity, I is the area momentof inertia, ρ is the beam material density, and A is the beamcross-section area. ( a ) Show that ω n is proportional to theantenna radius R . ( b ) If the antenna is steel, with L = 60 cmand D =4 mm, estimate the natural vibration frequency, inHz. ( c ) Compare with the shedding frequency if the carmoves at 65 mi/h.
- 3) A concrete coated steel gas pipeline is to be laid between two offshore platforms in 100 m water depthwhere the maximum environmental conditions include waves of 20 m wave height and 14 s period. Thepipeline outside diameter is 46 cm, and the clay bottom slope is 1 on 100. Determine the submerged unitweight of the pipe. Assume linear wave theory is valid and that the bottom current is negligible.This is regarding Forced Vibrations and Ordinary Differential Equations.Determine the reverberation time of a room whose dimensions L=20m, W=13m, and H=8m with a triangular ceiling of height 2m. The wall is made of marble with absorption coefficient of 0.03, the floor is covered with carpet (13m X 13m) with an absorption coefficient of 0.4, the ceiling is covered with plaster and lathe having 0.70 absorption coefficient. The floor is tiled with an absorption coefficient of 0.4. The sliding window on both sides is open half with a dimension of 2m X 10m and 0.075 absorption coefficient. The door (1.8m X 0.7m) has an absorption coefficient of 0.01. The windows is covered with blinds having 0.5 absorption coefficient half roll upward. A window type air-condition unit (W=470mm, H=340mm, D=600mm) is mounted at one side wall 6.5m from the floor to the base of the ACU with absorption coefficient of 0.35 and a refrigerator with dimensions 2ft X 2ft X 7ft is present in the room with 0.15 absorption coefficient. Use Fitzroy Equation.
- A tube well fully penetrating a confined aquifer has a maximum discharge capacity of 3000 liters per minute. The thickness of the aquifer is 60m. Design the minimum length of the well screen, assuming the effective open area of the screen to be 17% and 2 the diameter of the screen to be 20 cm. Assume also the safe screen entrance velocity to be less than 2.75cm/sec.A series of waves impinge on a wave -converting device is 500 m long .the period is 10s and the wave amplitude is 2.6 m determine the power generated per unit length (the density of sea water is 1030 kg/m^3) Typed and correct answer please. I ll rate accordingly.Engineering Mechanics Given: P=555N x=0.5m y-0.79m theta=36.2
- A shaft having length equal to 10 m and diameter equal to (50+ 01) mm is simply supported at both ends. The shaft carries four masses (150 + 01) kg, (200 + 01) kg, (250 + 01) kg and (300 + 01) kg. These masses are located at a distance of 1.5 m, 2.5 m, 5.5 m and 7.5 m from the left hand side support, respectively. The modulus of elasticity, E, for the material of the shaft is 200 GN/m2 and mass density for the shaft material is 7500 kg/m3. Determine critical speed of the shaft in revolutions per minute for the following two cases: Effect of the mass of the shaft is neglected. Effect of the mass of the shaft is considered. What is the usefulness of the answers determined in this problem?As shown in the figure below, a string attached to a vertical wall passes over a pulley at the end of a horizontal rod, and supports a sphere. The horizontal rod has a length L = 0.320 m, the mass of the sphere is M = 1.20 kg, the string makes an angle ? = 38.0° with the rod, and, when the string is plucked, the fundamental frequency of standing waves in the portion of the string above the rod is f = 70.0 Hz. Determine the mass of the portion of the string above the rod (in g). Answer:___________ gIt is necessary to propose the design of the base of a Chiller that has a weight of 1.5 tons.The proposed structural element must have a natural frequency between 10 rad/s and 15rad/s.