Problem 1 (30 Points) Consider the following 2 scenarios. In scenario 1, a mass m slides on a cylindrical surface of radius R. In scenario 2, a mass m hangs at the end of a thin massless rod of length R. In both scenarios, there is no friction either on the surface (scenario 1), or at the pivot point of the pendulum (scenario 2). Also in both scenarios, there is one generalized coordinate, . R Scenario 1 R m R g Scenario 2 m HINT: In both scenarios, it is much easier to choose your datum for potential energy as the center of the bowl (scenario 1), or the pivot point of the pendulum (scenario 2). Part I a) Determine the Lagrangian for each system. DO NOT FIND THE EQUATIONS OF MOTION (5 points) b) What can you say about the systems based on the Lagrangian? (2 points) c) Solve for the equations of motion for both systems. (8 points) Part II Now, for scenario 1, introduce an additional coordinate and treat it as a nonholonomic system to determine the normal force acting on the mass. a) What is the new coordinate that you must introduce? (2 points) b) Write the Lagrangian for the new nonholonomic system. (3 points) c) Write the constraint forces for each generalized coordinate. (5 points) d) Solve for the new equations of motion given all of the information about the system's constraints. (5 points)

Must use equation of motion and please include free body diagram. Thank you!

attached is a past paper question in which we werent given the solution. a solution with clear steps and justification would be massively appreciated thankyou.

Hi second question please. This is an engineering statics problem.

Using equation of motion and please include free body diagram. thank you!

Lessons: Static of Rigid Bodies, Force Vector, Addition of a System of Coplanar Forces, Cartesian Vector, Etc.   Kindly answer the following with complete solution. Please also draw the free-body diagram or illustration of your figure.   Make sure to write with understandable hand-writing. Please send a clear picture of complete solution. I need the answer within an hour at least. I'll rate you with a like/upvote.   Thank you.

For this problem, take a look at Figure 2 below. A disk with uniformly distributed mass m, radius R, and center of mass at point O is connected to a combination of springs at point P, which are then connected to a fixed wall. The disk rolls without slipping at point Q along an inclined plane that is at an angle a from the horizontal. Gravity acts in the vertical direction (towards the bottom of the page). ₁ is the linear coordinate of the point O along the inclined plane. The positive direction of ₁ is as shown. When the springs are undeflected, *₁ = 0. An angle , about the instant center of rotation, is shown. You may assume that the motion (and therefore angle ) is small. puny m Massless structure between springs R Figure 2: System schematic. Your tasks: A Draw the FBD for the disk. Don't forget the forces at point Q B Derive the equation of motion with as the dynamic variable. Be sure to put it in input-output standard form (inputs and constant forces on the right, things related to…

Lessons: Static of Rigid Bodies, Force Vector, Addition of a System of Coplanar Forces, Cartesian Vector, Etc.   Kindly answer the following with complete solution. Please also draw the free-body diagram or illustration of your figure.   Make sure to write with understandable hand-writing. Please send a clear picture of complete solution. I need the answer within an hour at least. I'll rate you with a like/upvote.   Thank you.

3. 3-46. In a motion capture study of a runner, one frame shows the subject support- ing her weight on one leg, as shown in Fig. P3.46. The length of the foot Ankle 30° 60° . Knee x Toes (a) During a motion capture study. Figure P3.46 Position of the runner's leg. segment (from ankle to toe) is 8 in. and the length of the lower leg (from ankle to knee) is 18 in. (a) Given the angles shown in Fig. P3.46(a), find the position of the knee if the runner's toes touch the ground at the point x = y = 0. (b) Now suppose that the same leg is positioned such that the knee is located in the second quadrant and oriented in the knee-down position (clockwise direction), as shown in Fig. P3.46. If the toes are located at P(x, y) = (-6.25 in., 25 in.), de- termine the values of 0₁ and 0₂. (-6.25, 25) Knee 19₂ Ankle y, in. Toes 0₁ (b) To find 0₁ and 0₂. x, in.

need help with Part D Please