Determine the motion expressions for each of the systems shown below by using the Euler-Lagrange equation. not skiping steps please explain i do not understand yet Pendulum of length (l) and mass (m) whose support rotates in a circle of radius (a)  in a vertical plane, with constant angular velocity ω as shown in the figure

Q: 2. The figure below shows three points in the operation of the ballistic pendulum. The projectile…

A: In the given system, the pendulum is at rest and the ball is moving with an velocity vi towards the…

Q: A solid disc with radius R is connected to spring at point (d) distance above the center of disc.…

A:

Q: The uniform rod (length 0.7 m) in figure rotates about an axis through one end, with a rotational…

A: Given Data⇒ Length of the uniform rod is L=0.7 m Rotational inertia of uniform rod is I=0.13 kg-m2…

Q: Given a moving cart (ż ‡0) with a pivoting bar. The cart is at a distance from the fixed wall and…

A: Given: To find: Inertial frame of reference Position of P wrt to frame e Velocity and acceleration…

Q: The rope shown in the figure below is wound around a cylinder of mass 4.0 kg and I = 0.020 kg m2,…

A:

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: QUESTION: A disk of mass m of radius R is mounted on a swivel joint L from the center of gravity as…

A:

Q: In the figure below there is one larger disc centred in O of radius 10 cm, a smaller disc centred in…

A:

Q: Tu) Ny Na DL

A: First of all reflect all impedances on the right to the viscous damper Then Take all impedances  and…

Q: Determine the governing equation of motion for the system shown below as well as zeta, wn and tau D.

A: The given is as shown below,   Let the rod AD is compressed by a small amount then the spring force…

Q: ₁ mm [₁ mm A WCD D B e cylinder A is rotating with an angular velocity of 4 rad.s-1, determine the…

A:

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

A:

Q: A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating…

A: Given:ω=100 rad/s I=10 kg-m2r=100 mv=20 m/s

Q: A circular solid disc of uniform thickness 20mm, radius 200mm and mass 20kg, is used as a fly wheel.…

A:

Q: Find the equations of motion for a lever of length 2a and of mass M rotating around its tip 8.₁ 20

A: The length of arm, L = 2aThe magnitude of mass = M

Q: A submarine is rolling under seawater whose radius of gyration is 12 m and period of oscillation of…

A:

Q: Q Find the egquations of motion of the vi brating undamped system Lagrange method. Fig be low ,…

A: If the speed of masses m1 and m2 are x1˙ and x2˙ respectively then,   The total kinetic energy of…

Q: Textbook P4.4 For the mechanism shown, determine the speed of point C at the instant 0₂ = 130°.…

A:

Q: v of the disc when it reaches position B

A: Given; As per given figure;   The speed v of the disc when it reaches position B ?Where,  A circular…

Q: (b) The total acceleration at t= 5 s is: * O 60 mm/s2 O 62 mm/s2 O 62.64 mm/s2 O 60.56 mm/s2 O 61.74…

A: velocity The velocity of an object is the rate of change of its position with respect to a frame of…

Q: Consider a slider crank mechanism with nonzero masses and inertia. A constant torquetis applied on…

A: A four-link system with three revolute joints and one prismatic, or sliding, joint is known as a…

Q: ) Find the equation of motion of the system in terms of the given parameters. b) Since M=4 kg, m=1…

A: For solution refer below images.

Q: Question J. fv x(t) オ Derive the equation of motion- ewe

A: For solution refer below images.

Q: A turbine motor of the ship shown in Figure Q3 has a mass of 3 tonnes with 0.5 m radius of gyration.…

A:

Q: Euler's second law of motion leads to:

A: Option (d) is correct. a straightforward relationship between the applied moment and change of…

Q: An object of mass 350 gm. is attached to a light cord revolves in a horizontal circular path as in…

A: Write the given data with suitable variables. m=350 g=0.35 kg1000 g1 kgT=35 N

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…

A:

Q: A homogeneous beam AB weighs P, where a point is a rope wound around a homogeneous cylinder. The…

A:

Q: Derive the kinetic energy equations and the mass equivalents of the two-system shown. -Thin disk of…

A:

Q: Fixed Fixed End End L/6 i L/6 2L/3 k- k< Point mass, M Uniform rod of mass, m Fixed End

A:

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: A wheel of radius (r-3) is placed as shown in figure. The wheel spins with constant angular speed…

A: Given Data ω1=4 ω2=5 r=3 Now for the lower point, wheel angular speed ω2 is only to be considered…

Q: 5 Derive the differential equation governing the motion of the system of Figure 9.6 using 0 as the…

A: For solution refer below images.

Q: b) Draw the free-body diagram and derive the equation of motion using Newton's second law. Also,…

A:

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.