F g K, K2
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Consider the system below with physical parameters M = 1.3, K1 = 7, K2 = 3, g = 9.81
a) Develop the dynamic equations using the Lagrangian approach
b) Explain which are the potential forces of this system
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- The following system is 2 degree of freedom system that consists of a moving block having mass m,, and an inverted pendulum of mass m2 that vibrates in the angular direction around block m1. The m2 inverted pendulum is constrained by a torsional spring k2. Determine the equation of motion of the system in the matrix form. kl kl www m1GROUP PROBLEM SOLVING Given: A 10-kg block is subjected to a force F=500 N. A spring of stiffness k=500 N/m is mounted F = 500 N against the block. When s = 0, the block is at rest and the spring is k = 500 N/m ssed. The contact surface uncomp is smooth. Find: Draw the free-body and kinetic diagrams of the block. Plan: 1) Define an inertial coordinate system. 2) Draw the block's free-body diagram, showing all external forces applied to the block in the proper directions. 3) Draw the block's kinetic diagram, showing the inertial force vector ma in the proper direction. ALWAYS LEARNING Dynamics, Fourteenth Edition in SI Units R.C. Hibbeler Copyright ©2017 by Pearson Education, Ltd. PEAR SON All rights reserve 21A 2.5 kg ball is launched into projectile motion by a slanted spring. The spring is compressed by 28cm, has a spring constant of 1200 N/m, and is slanted at a 42˚ angle. The ball leaves the spring at ground level. a) Determine the velocity at the moment the ball leaves the spring. b) Determine the maximum height above the ground reached by the ball. c) Determine how far horizontally the ball travels before coming back down to the ground.
- A block of mass m starts from rest at a height hand slides down a frictionless plane inclined at angle with the horizontal, as shown below. The block strikes a spring of force constant k. Amm mProblem 2 Consider the block of mass m, connected to a spring of spring constant k and placed on a inclined plane of angle a. Let la be the length of the spring at equili brium, and r be the elongation. The block oscillates and at the same time is rotating around origin 0, in the plane of the inclined, by a variable angular velocity . 1. Calculate the degrees of freedom of the block 2. What is the kinetic energy of the block 3. What is the potential energy of the block 4. Write the Lagrangian function (don't derive the Euler Lagrange equa- tions) k reference plane m o'For the system below, let k = 200 N/m, b = 20 N*s/m, and m = 0 kg. For the following cases, sketch the displacement graph over time and define the energy stored in the system at the beginning and at steady state. a. x(0) = 0; f(t) = 0 b. x(0) = 0.3m; f(t) = 0 C. x(0) = 0m; f(t) = 25 N m = 0 k ий 1+1 f(t) b
- A block of mass m = 0.72 kg attached to a spring with force constant 119 N/m is free to move on a frictionless, horizontal surface as in the figure below. The block is released from rest after the spring is stretched a distance A = 0.13 m. (Indicate the direction with the sign of your answer. Assume that the positive direction is to the right.) (a) At that instant, find the force on the block. N (b) At that instant, find its acceleration. m/s²I'm doing calc1 by myself right now and not sure where to start with this problem: Here are the questions: An object attached to a spring swings vertically around its equilibrium position. The height of the object relative to its position of equilibrium is given by the following function: h(t)=(e^-(x/10)*100sin(x)-10cos(x))/101 *(See photo i have provided)* a) Give the object movement for the first 10 seconds. I know i can find the speed of an object if i have it's acceleration. But how do i find it's movement fom it's height? I have done the integral of the height's equation and it's -(100e^-(x/10)(20sin(x)+99cos(x))/10201+Constant b) Give the total distance traveled by the object during the first 10 seconds I would assume this is something along the lines of finding the final positition of the object and the initial position and substracting them? c) Give the total distance that will be traveled by the object from time t = 0. at this point i am clueless to what i should find I…A particle moves with ω =constant and r = r0eβt where r0 and β are constants. For what values of β is the radial force zero?
- A particle of mass m = 1.18 kg is attached between two identical springs on å frictionless, horizontal tabletop. Both springs have spring constant k and are initially unstressed, and a particle is at x = 0. a) The particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown. Show that the force exerted by the springs on the particle is: Overhead view X-0- L F=-2kx|1- Vx+L b) show that the potential energy of the system is U(x)=kx²+2kL(L-Vx²+L*) c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 N/ m. d) If the particle is pulled 0.50 m to the right and released, what is its speed when it reaches x = 0? ww wwwwwwwA block of mass m = 0.71 kg attached to a spring with force constant 106 N/m is free to move on a frictionless, horizontal surface as in the figure below. The block is released from rest after the spring is stretched a distance A = 0.13 m. (Indicate the direction with the sign of your answer. Assume that the positive direction is to the right.) (a) At that instant, find the force on the block. N (b) At that instant, find its acceleration. m/s? Need Help? Read Ithelp please