A car is modeled as shown in Figure. Derive the equations of motion and find matrix M, C, and K. Mass = M, mass moment of inertia = JG .000 m1 k₂ F1 1 k2 000 k₁ k₁ m2 F2, X2 ell
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- A flywheel is fitted to a multi cylinder engine, which runs at a mean speed of 360 r.p.m. If the speed varies from 6 % above the mean to 2 % below it and the fluctuation energy is 1200 kN-cm, If the radius of gyration is 20 cm, find (i) mass moment of inertia of the wheel and (ii) mass of flywheel. The mass moment of Inertia in Kgm2 is Mass of the flywheel in kg isA structure has a mass of 10 kip/g and a stiffness of 10 kip/in. The acceleration of gravity, g, is 386.1 in/s2. Provide the period of the structure in seconds.An engine flywheel has a mass of 6.5 tones and the radius of gyration is 2 m. If the maximum and minimum speeds are 120 r. p. m. and 118 r. p. m. respectively, find maximum fluctuation of energy.
- [20] A crane that is 10 meters long is rotating (while loaded), at 1 radians/sec. It is stopped instantly (in 0.1 radian) in the position shown. Due to momentum the load continues to swing. Ignoring the deflection of the crane for this problem. (list all assumptions). The load is 750 lbs. a) The weight of the 10 m crane boom is 3000 lb and the mass moment of inertia is 80 lb ft s^2 about the centroid. Using the parallel axis theory find the mass moment of inertia around the point of rotation. Parallel axis theory can be found in appendix B formula B.6 (pg A9). b) Determine the maximum VERTICAL distance through which the load will swing. (Use the principle of work and energy with the work done by the weight. Two positions needed). c) What is the normal acceleration of the weight immediately after the crane stops (magnitude and direction)? d) What is the maximum energy that can be transmitted back to the crane (boom and load)? e) What forces and moments are there on the boom at the point…The inverse pendulum system given in the figure is freeDraw a diagram of the object and moveGet the equation (the mass of the pendulum m,moment of mass inertia is ? = (1/3)??2)Classical Dynamics of Particles and Systems Problem: A particle of mass m sits on the top of a frictionless sphere of mass M. The sphere is free to Slide on the frictionless ground.Let θ be the angle at which the radius to the particle makes with the vertical. Find the equation of motion for o Also, find the force of constraint in terms of θ and θ (theta dot/theta with dot above it). Also: Generate [x,y], [Vx,Vy], L= T-U
- The Newton's lows of motion for rigid body yields…….scalar equations describing the planar motion of the body: A) one B) two C) three D) sixA turntable is a uniform disc of mass 2 kg and radius 1.3 x 10-1 m. The turntable is spinning at a constant rate of = 0.5 . The motor is turned off and the turntable slows to a stop in 8.0 s with constant angular deceleration. Find the (a) moment of inertia of the turntable; (b) initial rotational kinetic energy; (c) angular deceleration of the turntable while it is slowing down; (d) total angle in radians that the turntable spins while slowing down; and (e) magnitude of the frictional torque.A crane that is 10 meters long is rotating (while loaded), at 1 radians/sec. It is stopped instantly (in 0.1 radian) in the position shown. Due to momentum the load continues to swing. Ignoring the deflection of the crane for this problem. (list all assumptions). The load is 750 lbs. a) The weight of the 10 m crane boom is 3000 lb and the mass moment of inertia is 80 lb ft s^2 about the centroid. Using the parallel axis theory find the mass moment of inertia around the point of rotation. b) What forces and moments are there on the boom at the point of rotation?
- Form the Equation of Motion (EOM) [ma + cv + kx = p(t)] for the following structure.The mass moment of inertia I of a homogeneous sphere about its diameteris I = (2/5)m R², where m and R are its mass and radius, respectively. Find thedimension of I in terms of the base dimensions of (a) a gravitational [FLT] systemand (b) an absolute [MLT] system.1) A cylindrical rod of constant shear modulus, G is of length L and located between z=0 and z=L. It has a polar moment of inertia given by J=(Jo)/(1-Z/L) and t=-sin(πZ/2L)where Jo is a constant.The boundary conditions are dΦ(o)/dz =0 AND Φ(L)=0 Find Φ(z) and graph (1/GJo)Φ(Z), and (1/GJo)(dΦ(Z)/dz) ?