Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equ masses m1 is attached to the opposite sides of the shaft in the vertical plane as shown in figure. Consider m= 1 kg, e 50 mm, e1= 20 mm, b = 0.3 m, a = 2 m and a1 = 2.5 m. For the system to be dynamically balanced, m1 should b _kg.
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- 3) Consider this car, which can be modelled as a rigid bar with its centre of mass C.G. not coinciding with its geometric centre (m= 1000kg, 11m; /2 = 1.5m ), and supported by two springs, k = kx=20kN/m, as shown in Figure Q1 (a) Describe the system in term of degree of freedoms (b) Draw the free body diagram for the system to derive the equations of the vibration motion (c) Determine the mass matrix and stiffness matrix of the system. (d) Determine the nature frequencies of the system Bounce C.G. Pitch -1/2- Figure Q1Considering the figure shown, determine the equivalent spring constant of a spring that will represent all of the given springs such that its deflection is along a vertical path with the mass. k1=1N/m k2=2N/m k3=3N/m k4=4N/m and k5=5N/m. (answer in N/m) * k2 m kg k4A moment M is slowly increased as it is applied to the disk shown in Fig. tential energy of the system with respect to a reference at e = 0° as the disk is rotated to the position 0 = 45°. The spring (k = 10 lb/in.) is unstretched at e = 0°. Determine the change in po- W = 50lb 16 in. M 8 in. www A
- A 0.20 kg horizontal beam has length L=0.8 m. It is supported by a fulcrum at d=0.55 m from the left end. A 0.15 kg mass ml is suspended at xl=0.15 m from the bar's left end. Another mass mr is suspended at xr=0.65 m from the bar's left end. The system is in equilibrium. How heavy in kg is the mass mr on the right side? Hint: the bar's gravity has a torque if it is not supported by the fulcrum at exactly half way.Consider the system shown in the following figure, which is pivoted at point O. Suppose the system is moving in a horizontal plane. Assume that a0.4 m,b-1m M=2 kg the mass of the bar m 4 kg. k10 N/m, c 93 kg/s and F(t)= F6 (t) N where F = 3Ns Assume zero initial conditions and the moment of inertia of the bar about point O to be Determine the mnaximum tip response amplitude in mm. ww- Rigid bar M F() 6154 mm 13.90 mm 8.93 mm 83.37 mm 19.85 mm O00 00The first figure gives spring force Fx versus position x for the spring-block arrangement of the second figure. The scale is set by Fs = 190 N. We release the block at x = 13.0 cm. How much work does the spring do on the block when the block moves from x; = +9.0 cm to (a) x = +5.0 cm, (b) x = -5.0 cm, (c) x = -9.0 cm, and (d) x = -11.0 cm? -x (cm) -2 -1 -F, X* = 0 Block attached to spring F = 0 (a) x positive F, negative F (b) x negative F, positive (c)
- 3) Consider a car, which can be modelled as a rigid bar with its centre of mass C.G. not coinciding with its geometric centre (m= 1000kg, 1 = 1m; /2 = 1.5m), and supported by two springs, kr = kr = 20kN/m, as shown in Figure Q3 (a) Describe the system in term of degree of freedoms (b) Draw the free body diagram for the system to derive the equations of the vibration motion (c) Determine the mass matrix and stiffness matrix of the system. (d) Determine the nature frequencies of the system System respon Bounce C.G. Pitch Figure Q3Th lamp , mass = 10 Kg, is suspended in the position shown. The undeformed length of spring AB is 0.84 m and the spring has a stiffness of K = 784 N/m. For L= 2.8 m find Tension in cable AC , Internal force in spring AB, length of ACConsidering the figure shown, determine the equivalent spring constant of a spring that will represent all of the given springs such that its deflection is along a vertical path with the mass. k1=1N/m k2=2N/m k3=3N/m k4=4N/m and k5=5N/m. (answer in N/m) * k2 m k3 k5 k4
- Two massless springs with different spring constants k₁= 100 N/m and k₂ = 10 N/m are aligned vertically, as shown in figure 1. A block of mass m = 0.12 kg is placed on the bottom spring. The distance between the top of the box and the top spring is h = 0.35 m. You compress the bottom spring Ay = 0.3 m from its equilibrium position (figure 2). When you let go, the box flies up (figure 3) and compresses the top spring (figure 4). Treat the upward direction (↑) as positive, such that the compression of the top spring is a positive displacement. What is the maximum compression of the top spring due to the flying box? Give your answer in units of meters to 2 decimal places. Use g = 9.8 m/s^2. Assume air resistance is negligible. T h EW Ay (2) www Backup link to image (opens in new tab). fumand M риту 4 ² ↑ M ? wwwA gymnast holds a steady handstand on the top of the uneven bars as shown. ITNEASTICS a. As long as the gymnast grasps the bar and holds this position, how many degrees of freedom are represented by this system? (explain) b. The 2.5 m bar has a 3.5 cm diameter, a linear density of u = 8 kg/m and a modulus of Elasticity of E = 8000 MPa, and the gymnast has a mass of 45 kg. What is the static deflection of the midpoint of the bar? c. What is the dynamic equation for the vertical motion of the bar about the static equilibrium point as the gymnast holds this position? d. What is the characteristic equation and natural frequency of the motion?In the given fig shows the suspension system of a freight truck with a parallel-spring arrangement. Find the equivalent spring constant of the suspension if each of the three helical springs is made of steel with a shear modulus G = 120GPaand has five effective turns, mean coil diameter D = 50 cm, and wire diameter d = 5 cm