A foot pedal mechanism for a machine is crudely modeled as a pendulum connected to a spring as illustrated in Figure. The purpose of the spring is to keep the pedal roughly horizontal. Derive the differential equation of this system assuming that the angular deflections are small, such that the spring deflection can be approximated by the arc length, that the pedal may be treated as a point mass and that pendulum rod has negligible mass. The values in the figure are m = 0.5 kg, k = 2100 N/m, g = 9.8 m/s², ₁ = 0.2 m and l₂ = 0.3 m. 12 k Ꮎ 12 g m

Please solve with applying newton law. I need full work with full steps please

A pendulum is made up of a spring with a mass attached to the end. The spring is arranged to lie in a straight line, by wrapping the spring around a massless bar. The equilibrium length of the bar is “l”. Using lagrange’s equations, find the equations of motion.

I In this problem, consider the figure below. A disk with radius r, mass m, and moment of inertia of Io about the point O is on an inclined plane, with the translational coordinates and y and rotation angle 0, as shown. The direction of gravity is shown, and the incline angle is a. A constant input torque is applied at the point O in the direction shown, and it is opposed by a damping torque from a bearing with value co in the direction shown. The point P represents a point of instantaneous contact, rolling without slipping. Your tasks: Direction of Gravity M(t) co 0 P x Mass: m Figure 2: System schematic. Moment of Inertia about 0: lo a: Incline Angle A Draw the FBD for the disk. B Derive the equation of motion with the rotation angle as the dynamic variable. 0 C Take the Laplace transform, and solve for (s), letting the initial conditions be 0(0) = 0 and (0) = 0. Remember that a constant is a step function for a one-sided Laplace transform. D Given your expression for (s), find the…

Block String Rod Disk Mech 3. As shown above, a uniform disk is mounted to an axle and is free to rotate without friction. A thin uniform rod is rigidly attached to the disk so that it will rotate with the disk. A block is attached to the end of the rod. Properties of the disk, rod, and block are as follows. Disk: Зт, radius R, moment of inertia about center ID = mR² mass = %3D Rod: m, length = 2R, moment of inertia about one end IR mR? mass = Block: mass = 2m The system is held in equilibrium with the rod at an angle 0, to the vertical, as shown above, by a horizontal string of negligible mass with one end attached to the disk and the other to a wall. Express your answers to the following in terms of m, R, 00, and g. (a) Determine the tension in the string.

Figure Q9 shows part of a system with many degrees of freedom. Write the equation of motion for m₂. Specify the assumptions that you may need to consider in determining the relative displacements and subsequent spring forces. ■ ■ ■ Kn-1 i M Fn-1 Kn Juny mn-1 mn kn+1 Fn mn+1 Kn+2 n

Machine Dynamics: In the mechanism in the figure; The 2nd limb in the horizontal position rotates with a constant angular velocity of 100 rad/s under the effect of external torque T12.Obtain the equations of change of axial internal force, shear force and bending moment in limb 3 due to inertia and bond forces at the specified position, ignoring frictions.(O2 joint point is the center of gravity of limb 2) "Detailed Solution Please"

Obtain the number of degrees of freedom of the mechanism shown in Figure to

A simplified SDOF model of a vehicle suspension system is shown in below Figure. The mass of the vehicle is 500 kg. The suspension spring has a stiffness of 100,000 N/m. The wheel is modeled as a spring placed in series with the suspension spring. When the vehicle is empty, its static deflection is measured as 5 cm. (a) Determine the equivalent stiffness of the wheel (b) Determine the equivalent stiffness of the spring combination. (c) Determine the natural frequency fn of the system ks kw m ww Suspension spring Wheel I stiffness

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