find the equations of motion using the lagrange equations of motion. The main rod has length l and mass m, the left spring has spring constant k and right spring has spring constant 2k

Q: Q1) Derive the equation of motion of figure 1. 2k Slender bar of mass m Rigid massless link Thin…

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Q: Problem 4: Use the principle of virtual work to determine the equation of motion for the system…

A: For solution refer below images.

Q: The ends of a 0.25kg rod AB are constrained to move along slots cut in a vertical plate as shown. A…

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Q: HW2 A uniform disc of 80 mm radiuse has a mass of 2000 g. It is mounted centrally in bearings which…

A: Given d=80mm r= 40mm  = 0.04m                                     m= 2000g = 2kg N=550rpm…

Q: e mechanism shown in Figure P8.1 mass of 3.0 lbm and polar mass m tia of 0.04 lb-in-sec2 about its…

A: T is torque because of moment of inertia and it acts upper direction and rotate in…

Q: the system shown in Figure 1, assume that the rod pivoted at point P is massless and perfectly…

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Q: 3- Draw the free-body diagram and derive the equation of motion using Newton s second law of motion…

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Q: k m

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Q: Find the equation of motion of the system where G is mass center and e is the distance to the…

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Q: A rod of mass M and length L is pivoted at point O, as shown below. At the end f each rod is a…

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Q: Derive the differential equation of motion for the system shown in Figure (). Neglact the mass of…

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Q: A conical pendulum having a 2 kg mass attached at the end of the string is rotating at a constant…

A: m=Mass of conical pendulum=2 kgV=constant speed=4 m/sR=Horizontal Circle Radius=1 m

Q: Find the angular frequency of motion of disc of mass m and radius r for small motion (Assuming that…

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Q: For the system shown in Figure Q 4: (i) Draw the free body diagram (i1) Formulate the equation of…

A: Consider a system having mass M attached by two spring and fixed at another end on the wall.…

Q: Q4) Derive the equation of motion of figure 4. www 2c 一十 Slender bar of mass m Figure 4

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Q: Two homogeneous rods ABC and OB of mass 14 kg/m Rajah S4a are welded together to form a T-shaped…

A: λ=14 kg/m, ω=3rad/s, M=8Nm Position of COMycm=140.52+14x0.514+14ycm=3x0.54ycm=0.375m change in…

Q: The pivot of a simple pendulum (length I, mass m) is attached to a disc of radius R, which rotates…

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Q: Q2. A flywheel weighing 50KN and having radius of gyration 1m looses speed from 400rpm to 280 rpm in…

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Q: 2. A uniform bar of length 2a, and mass m is linked to a uniform cylinder of radius b and mass M. In…

A: Given,  The length of bar, L = 2a The radius of cylinder, r = b The mass of cylinder, m = M

Q: find the equations of motion using the lagrange equations of motion. The main rod has length l and…

A: Given : To find : equation of motion

Q: Q4: Consider the system shown in the figure. k = 250KN / m M c = 6000 N.s/m m =1000 kg m, =2 kg e =…

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Q: The ends of a 0.25kg rod AB are constrained to move along slots cut in a vertical plate as shown. A…

A: For solution refer below images.

Q: Consider the system below. Calculate the kinetic energy of this system. Assume that pulley otates…

A: Drr

Q: Find the equations of motion for the system, where m1 and m2 are the masses of the two objects, k1,…

A: The springs with spring constant, k1, k2, k3 The equilibrium displacement of the three springs, l1,…

Q: Find the radius of gyration (KG) of a compound pendulum if the time period (T) is 1.5 second and…

A: Compound pendulum: When any rigid body starts oscillating due to the effect of the force of gravity…

Q: A pendulum consisting of a rod of mass 2m of mass 3kg and a ball of mass 1kg and a radius of 0.3m…

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Q: Q4) Derive the equation of motion of figure 4.

A: Given Data: The mass of the slender rod is m. The spring constant of the springs is k. The damping…

Q: Find the equation of motion of the following spring system.

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Q: A bar of 30 kg mass is in the rest position for the position θ = 0 °, for which the spring is in its…

A: Given: The mass of bar, m = 30 kg

Q: A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given…

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Q: A helical spring has a stiffness of of 25 kN/m. If a mass of 100 kg is attached to its free end,…

A: Given data: Stiffness of spring = 25000 N/mmass = 100 kg

Q: Find the radius of gyration (KG) of a compound pendulum if the time period (T) is 1.5 second and…

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Q: 5. The pendulum shown below consists of a 30 kg point mass at the end of a uniform bar with mass m =…

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Q: a 4.8 kg block is resting at the top of a 30 degree slope of height 1 m it is attached to a…

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Q: Find the equation of motion using the Lagrangian method? Problem 3.2 K1 wwwm K2 C www M2 O O F(t)…

A: we have lagrangian euation as ∂∂t∂L∂x·-∂L∂x=F(t)..............................(1)here L= Lagrangian…

Q: A cart of mass m is pushed against an ideal spring (Obeying Hooke's law) of spring constant k. The…

A: Applying the Conservation of  Energy  from Point A to B 12×k×d2=12×m×V2k×d2=m×V2V2=km×d2V=km×d

Q: (97) Derive the equations of motion of the system shown in the figure below using Lagrange's…

A: To derive: The equation of motion using Lagrange's equation. Given: The mass of the circular…

Q: A spring-based toy gun is used to shoot a ball of mass M straight up. The ball is not attached to…

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Q: By determining the equivalent spring constant of the mass spring system given in the figure, we…

A: Spring 1 and 2 are in parallel. The equivalent spring constant for parallel connection is, k12=k1+k2…

Q: HW2 A uniform disc of 80 mm radius has a mass of 2000 g. It is mounted centrally in bearings that…

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Q: In the figure, two blocks hang at rest from a spring and rope attached to the ceiling. On the left,…

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Q: 4) A planet that has a hollow core consists of a uniform spherical shell with mass M, outer radius…

A: Given Data: The mass of the planet is M. The outer radius is R and the inner radius is R/2. Part…

Q: 6 kg The system shown in the figure consists of two masses attached to a massless road and rotates…

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Q: Figure 13 shows a simple model of a machine part, with an applied moment applied clockwise to the…

A: Lagrange’s equations is defines as the equation of motion of a mechanical system with multiple…

Q: Find the radius of gyration (KG) of a compound pendulum if the time period (T) is 1.5 second and…

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Q: k, K2 m k3 : ks K6 K4

A: Given  k1=k2=35 N/m, k3=k4=55 N/m, k5=70 N/m, and k6=20 N/m.

Q: A disk is attached by a spring to a pin. The disk can roll in the horizontal direction and the pin…

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Q: The 10 N cylinder moves in a frictionless pipe. Spring constants are k1 = 150 N / m and k2 = 200 N /…

A: Given, weight of the cylinder , W = 10 N spring constants , K1 = 150 N/m and K2= 200 N/m. d=0.5 m…