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3) (35 percent) Determine the differential equation of the system in the figure below...
04: Derive the differential equation governing the motion of the one degree-of-freedom system by using Newton's...
04: Derive the differential equation governing the motion of the one degree-of-freedom system by using Newton's method. Use the generalized coordinates shown in figure (5) (bar moment of inertia, 1-2 ml) Slender bar of mass m Figure (5)
solve with newton's method Q1: Use the equivalent system method to derive the differential equation governing...
solve with newton's method
Q1: Use the equivalent system method to derive the differential equation governing the free vibrations of the system of Figure below. Use x, the displacement of the mass center of the disk from the system's equilibrium position, as the generalized coordinate. The disk rolls without slipping, no slip occurs at the pulley, and the pulley is frictionless. Include an approximation for the inertia effects of the springs. Each spring has a mass ms. Use newton's method....
3) For the single degree of freedom system shown below: a) Use the equivalent system method...
3) For the single degree of freedom system shown below: a) Use the equivalent system method to derive the differential equation governing the motion of the system, taking χ as the Slender har of mass m generalized coordinate. Rigid 1 link b) If m-6 kg, M = 10 kg, and k=500 N/m, determine the value of c that makes the system critically damped. c) For the values obtained in part (b), determine the response of the system, x(t) if x(0)=...
determine the equivalent mass(meq)and equivalent spring stiffness of the system shown in the figure below using...
determine the equivalent mass(meq)and equivalent
spring stiffness of the system shown in the figure below using x as
the generalized coordinate
neral MES 382: Vibration & Noise Control Determine the equivalent mass (megl and equivalent spring stiffness (kea) of the syslem shown in the figure below using x as the generalized coordinate. b. ko Jo k2 k1
Please show work 3. Given a mass-spring-damper system, the 2kg mass is connected to two linear...
Please show work
3. Given a mass-spring-damper system, the 2kg mass is connected to two linear springs with stiffness coefficients ki- 100 N/m and ki 150 N/m and a viscous damper with b 50 Ns/m. A constant force of SN is applied as shown. The effect of friction is negligible. ki m b 3.1 [2pts] Determine the equivalent stiffness of the springs. 3.2 [3pts] Draw the free-body diagram of the system. Define the generalized coordinate and label your forces and...
ke Slender bar of mass m As shown in Figure 1, a uniform slender bar with...
ke Slender bar of mass m As shown in Figure 1, a uniform slender bar with mass m and length L is supported by a vertical spring at its right end while a mass block 2m suspended from its left end through a spring is supported by another spring. All these three vertical springs have the same stiffness k. If the downward vertical displacement x of the mass block and the clockwise rotation angle 8 of the bar are assumed...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
Use Newton's method to determine the differential equation of motion, for the system shown, in terms...
Use Newton's method to determine the differential equation of motion, for the system shown, in terms of the coordinates x and y. Jo is the moment of inertia for the pulley. Displacements x and y are zero when the system is in equilibrium. a) Show and properly label the (3) free body diagrams. b) Write and simplify to two EOMs for coordinates x and y Bonus: Write EOMs in matrix form for coordinates x and y 2r r 0 FO)
Xosin(ot) Shown in the figure below is a rigid pendulum bar of I= 1 m and...
Xosin(ot) Shown in the figure below is a rigid pendulum bar of I= 1 m and mass m, 1 kg attached to a roller, of mass m, = 0.2 kg, whose motion is described by X, sin(@t), Xo = 1 [m]. Model the pendulum bar as a uniform slender rod which has a moment of inertia with respect to its mass centre Ig given by m1/12. Use tangential-normal coordinate system to analyze the dynamics of the pendulum bar and use...
Question 4 The slender bars AB and BC of the linkage shown in Figure Q4 have...
Question 4 The slender bars AB and BC of the linkage shown in Figure Q4 have mass m and length I, and the collar C has mass m. A torsional spring at A which has a stiffiness of k, exerts a torque on the bar AB. Knowing that when o-0, the system is in equilibrium and the torsional spring which is attached to the slender bar AB is not twisted. If the system is perturbed a bit from equilibrium and...
04: Derive the differential equation governing the motion of the one degree-of-freedom system by using Newton's method. Use the generalized coordinates shown in figure (5) (bar moment of inertia, 1-2 ml) Slender bar of mass m Figure (5)
solve with newton's method
Q1: Use the equivalent system method to derive the differential equation governing the free vibrations of the system of Figure below. Use x, the displacement of the mass center of the disk from the system's equilibrium position, as the generalized coordinate. The disk rolls without slipping, no slip occurs at the pulley, and the pulley is frictionless. Include an approximation for the inertia effects of the springs. Each spring has a mass ms. Use newton's method....
3) For the single degree of freedom system shown below: a) Use the equivalent system method to derive the differential equation governing the motion of the system, taking χ as the Slender har of mass m generalized coordinate. Rigid 1 link b) If m-6 kg, M = 10 kg, and k=500 N/m, determine the value of c that makes the system critically damped. c) For the values obtained in part (b), determine the response of the system, x(t) if x(0)=...
determine the equivalent mass(meq)and equivalent
spring stiffness of the system shown in the figure below using x as
the generalized coordinate
neral MES 382: Vibration & Noise Control Determine the equivalent mass (megl and equivalent spring stiffness (kea) of the syslem shown in the figure below using x as the generalized coordinate. b. ko Jo k2 k1
Please show work
3. Given a mass-spring-damper system, the 2kg mass is connected to two linear springs with stiffness coefficients ki- 100 N/m and ki 150 N/m and a viscous damper with b 50 Ns/m. A constant force of SN is applied as shown. The effect of friction is negligible. ki m b 3.1 [2pts] Determine the equivalent stiffness of the springs. 3.2 [3pts] Draw the free-body diagram of the system. Define the generalized coordinate and label your forces and...
ke Slender bar of mass m As shown in Figure 1, a uniform slender bar with mass m and length L is supported by a vertical spring at its right end while a mass block 2m suspended from its left end through a spring is supported by another spring. All these three vertical springs have the same stiffness k. If the downward vertical displacement x of the mass block and the clockwise rotation angle 8 of the bar are assumed...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
Use Newton's method to determine the differential equation of motion, for the system shown, in terms of the coordinates x and y. Jo is the moment of inertia for the pulley. Displacements x and y are zero when the system is in equilibrium. a) Show and properly label the (3) free body diagrams. b) Write and simplify to two EOMs for coordinates x and y Bonus: Write EOMs in matrix form for coordinates x and y 2r r 0 FO)
Xosin(ot) Shown in the figure below is a rigid pendulum bar of I= 1 m and mass m, 1 kg attached to a roller, of mass m, = 0.2 kg, whose motion is described by X, sin(@t), Xo = 1 [m]. Model the pendulum bar as a uniform slender rod which has a moment of inertia with respect to its mass centre Ig given by m1/12. Use tangential-normal coordinate system to analyze the dynamics of the pendulum bar and use...
Question 4 The slender bars AB and BC of the linkage shown in Figure Q4 have mass m and length I, and the collar C has mass m. A torsional spring at A which has a stiffiness of k, exerts a torque on the bar AB. Knowing that when o-0, the system is in equilibrium and the torsional spring which is attached to the slender bar AB is not twisted. If the system is perturbed a bit from equilibrium and...
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