A 5-kg uniform rod CD of length
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- 2. The weightless rod carries two masses m. one at a distance L from the pivot or the other at 2L. If the rod is rotated by a small angle e and released, determine the following: a. the differential equation of motion of the system, and b. the natural frequency of vibration of the rod. (J. - mc?, where c dist amce from mass m to pivot 0.)arrow_forwardThe homogeneous rod OA is supported at point 0, and a mass of 2m is attached at the bottom of the system as shown. For small oscillations and by use of ENERGY METHOD;arrow_forwardA 4-lb uniform rod is supported by a pin at O and a spring at A and is connected to a dashpot at B. Determine (a) the differential equation of motion for small oscillations, (b ) the angle that the rod will form with the horizontal 5 s after end B has been pushed 0.9 in. down and released.arrow_forward
- Want in detailarrow_forwardTwo identical spring-mass systems A and B are coupled by a weak middle spring having a spring constant smaller by a factor of 100 (i.e. 100kmiddle = kA = kB). Mass A is pulled by a small distance and released from rest, while mass B is released from rest at its equilibrium position, at t = 0. Calculate the approximate number of oscillations completed by mass A before its oscillations die down first.arrow_forward2. A point mass m is strung on a vertical ring of radius R, and it oscillates freely with respect to its equilibrium point located at the lowest point of the ring. An external moment of force is applied that causes the ring to oscillate about its center in the form α = α₁ cost where a is the angle of rotation. Determine the general movement of the mass m, and under what circumstances this movement enters into resonance, detailing this phenomenon.arrow_forward
- 4. A student followed strictly correct procedure in the lab during the experiment of moment of inertia. He measured the mass and diameter of plastic cylinder with value of m = 0.36 kg and D = 0.1 m. The period of system without plastic cylinder is To = 0.667 s. The period of system with plastic cylinder T₁ = 0.92 s. Find: The spring constant K of the system. If a metallic cylinder and a plastic cylinder have same diameter and same thickness, which one has larger moment of inertia? Explain.arrow_forwardQ.1 The system shown below consists of a block of mass m and a cylinder of mass 2m. The block and the cylinder are joined by pulley arrangement as show. The coordinates x and y are dependent in which x = 2y. Use m= 2 kg. The angle 0 is any value between 0 and 90°. If the cylinder is pushed downward 20 mm and released a) find the subsequent response of the block, x(1) b) find the displacement and velocity of the block at t = 1 s. The specific value of k is given in separate excel sheet. K=1985 2m IT, x = 2yarrow_forwardA thin cylindrical rod of uniform mass m and length L is suspended from the ends by two massless springs with constants k1 and k2 (Distance L1 and L2 on either side of the center of mass of the rod). The motion of the center of mass is constrained to move up and down parallel to the vertical y-axis. It also experiences rotational oscillations around an axis perpendicular to the rod and passing through the center of mass (I is the moment of inertia with respect to said axis). be y1 and y2 the displacements of the two ends from their equilibrium positions, as shown in Fig. a) Find the motion's equation (consider k1=k2=k)arrow_forward
- Y2arrow_forwardsolve this without the application of MOMENTS please. the answer is attached alsoarrow_forward4- The block is supported by the spring arrangement as shown. The block is moved vertically downward from its equilibrium iggila position and released. Knowing that the amplitude of the resulting motion is 45 mm, determine the natural period and the frequency of the motion. Also, find the maximum velocity and the maximum acceleration of the block for each case of the following. 16 kN/m 10 ib/in. 16 kN/m 20 lb/in. : 25 b/in. 35 kg -16KN/m 16 lb/in. 12 b/in. 20 lb/in. 8 kN/m kN/m akg (a) (b) (c) (d)arrow_forward
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