Please be as detailed as possible cause I want to understand it.
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Please be as detailed as possible cause I want to understand it. Thanks! 14 Figure 1:...
A simple pendulum (mass M and length L) is suspended from a cart of mass m that moves freely along a horizontal track shown at right. You might find it helpful to introduce the dimensionless parameters η-m/M and wo- /g/L. a What are the normal frequencies of small oscillations of the system (0 <1)? b Find and describe the corresponding normal modes of the system. c The cart/pendulum systern is held at rest in the configuration x-0 and θ K...
(35pt) A kid is swinging on a swing (gravity is pointing down, see figure). The swing has a friction which is proportional to the velocity. Specifically: |Ffric| =(m/4)*sqrt(gl)*θ' . (3) (a) (5pt) Write down the equation of motion of the θ direction of the polar coordinates. (b) (30pt) Assume small oscillations and that the kid has the following initial conditions θ(t = 0) = θA and ˙θ(t = 0) = 0. (i) (10pt) Find the frequency of the oscillations as...
1) Consider a block of mass M connected through the massless rigid rod to the massless circular track of radius a on a frictionless horizontal table (see the Figure). A particle of mass m is constrained to move on the vertical circular track. The distance between the center of the circular track and the center of mass of the block of mass M is constant and equal to L. Assume that there is no friction between the track and the...
A plane pendulum of length L and mass m is suspended from a block of mass M. The block moves without friction and is constrained to move horizontally only (i.e. along the x axis). You may assume all motion is confined to the xy plane. At t = 0, both masses are at rest, the block is at , and the pendulum has angular deflection with respect to the y axis. a) Using and as generalized coordinates, find the Lagrangian...
The Problem The single pendulunm Consider the single pendulum shown below. There is a bob at the end of the pendulum, of mass For small oscillations in the case of a frictionless pivot and a rod with negligible mass, the motion of the pendulum over time can be described by the second-order linear ODE where θ is the angle between the rod and the vertical, g is gravity, t is the length of the rod and θ dag /dt2 Q1...
4. Consider a double pendulum with identical length, L and mass, m constrained to move in the x-y plane. Using the Cartesian coordinates, x and y write down the kinetic and potential energies of the system in terms of, and θ2. Find the Lagrangian and two corresponding equations for the system. Assume the angles 0, and 02 are both very small so that sin θ θ and cos θ 1 and state the approximate equations
Fresh answer please. Thanks in advance. Consider the following pendulum that consists of a massless straight rigid rod AOB with a point mass m attached at the top point B and a point massM attached at the bottom point A. The pendulum rotates without friction about point O and it is initially at vertical equilibrium. Two springs are attached at the top point B from one end and fixed at the other end. The springs are unstretched at t-0 and...
Lagrangian Mechanics: A pendulum of mass m and length l hangs from the rear view mirror in a car traveling with horizontal acceleration a. Assume the car starts from rest at time t=0. (Solve using Lagrangian Mechanics.) a) Draw a diagram of the situation. Write out the x and y coordinates of the position of the pendulum in the in terms of the angle of the pendulum, Φ, and the time t. b) Write out T, U, and L in terms...
A homogeneous ring of radius R and mass m can roll on a horizontal surface without slipping. It is attached at the center to a spring of elastic constant k and rest length 1, and can oscillate on the horizontal plane. See the figure below for a schematic presentation. k (i) What is the number of degrees of freedom of the system? [2] (ii) Compute the moment of inertia of the ring about an axis perpendicular to it and going...
Question 2 The pendulum shown in Figure 2 consists of a concentrated mass m attached to a rod whose mass is small compared to m. The rod's length is L. The equation of motion for this pendulum is Suppose that L 1 m and g 9.81 m/s2. Use MATLAB to solve this equation using symbolic and numerical techniques for, θ(t) for two cases: , θ(0)-0.5 rad and, θ(0)-0.8 rad. In both cases 0(0) 0. Figure 2- A pendulum [3 marks]...