Obtain the Lagrange equations of motion for a spherical pendulum, i.e., a mass point suspended by a rigid weightless rod.
Q: In the system shown in below figure, the inertia, J, of radius, r, is constrained to move only about…
A: The final answer is in Laplace transformation.
Q: A simple pendulum of length and bob with mass m is attached to a massless support moving vertically…
A: Given: A simple pendulum having length of string, λ Mass of bob is m and Constant acceleration, α…
Q: To measure the magnitude of the acceleration due to gravity g in an unorthodox manner, a student…
A:
Q: Consider the pendulum illustrated below. Consider the free body diagram for the bob. The restoring…
A: The force is restoring force therefore it can be written as: In the equation, the restoring force…
Q: A mass-spring-dashpot system has mass m = 2 kg, spring constant k = 9 N/m, and drag coefficient c =…
A:
Q: The system shown in Figure Q1 consists of two interconnected masses mi and mz. Both springs of…
A: Since you have have asked multiple question, we will solve the first question for you. If you want…
Q: A mass M=4kg is connected to a spring-dashpot system with spring constant k=10000N/m and a damper…
A: Given Data : M = 4Kg K = 10000 N/m Damper coefficient, c = 8N.s/m g = 9.8 m/s² Initial…
Q: 8.10** Two particles of equal masses m₁ = m₂ move on a frictionless horizontal surface in the…
A: The Lagrangian of the given system is,For m1=m2=m, the above equation can be written as follows:The…
Q: x(t) = . which means the system is (Use integers or decimals for any numbers in the expression.…
A:
Q: A uniform cylinder of mass M sits on a fixed plane inclined at an angle .A string is tied to the…
A:
Q: Problem 1: Assume that two variable forces F₁ and F2 are being applied to the following masses n₁…
A:
Q: Problem 2: A fisherman has caught a fish on his pole, and to keep the pole steady he has to apply…
A: Consider the Figure shown below.
Q: a) Show that the following equation is a solution to Newton's second law ΣF: = ma for a pendulum,…
A:
Q: Find the period of motion for a ball on a string moving with a constant speed of 4.01 meters per…
A: Assuming that the string forms a circle, and the ball is performing a periodic motion on this…
Q: I want you to draw this system for me from the description: I will consider a system with three…
A: consider a system with three pendulums of equal lengths, L, but with potentially different masses…
Q: A 1.19 kg ball is connected by means of two ideal strings to a horizontal, rotating rod. The strings…
A: Mass m=1.19 kg Right string, TR=29.5 N , angle Left string, tension= TL
Q: A block of mass m =1 is sitting on a table and is attached to a spring of strength k = 5 so that it…
A: Given information: The mass of the block (m) = 1 kg The strength of the spring (k) = 5 The…
Q: Show that the function x(t) = A cos ω1t oscillates with a frequency ν = ω1/2π. What is the frequency…
A:
Q: A pointlike body of mass m made of lead is fixed inside a homogeneous solid sphere of radius R and…
A: Given data The mass of the point-like body is m. The radius of the sphere is R The location distance…
Q: b) The following table gives the density of some different media and the speed of ultrasound through…
A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub…
Q: Problem 2: Suppose the massless rod in the discussion of the nonlinear pendulum is a string of…
A:
Q: A uniform rod of length 2.0 m, and 3.2 kg is suspended from a pivot a distance 0.2 m above its…
A:
Obtain the Lagrange equations of motion for a spherical pendulum, i.e.,
a mass point suspended by a rigid weightless rod.
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
- A cylindrical disc with a mass of 0.619 kg and radius of 0.575 m, is positioned such that it will oscillate as a physical pendulum as shown below. If the period of the small angle oscillations is to be 0.343 s, at what distance from the center of the disc should the axis of rotation be fixed? Assume that the position of the fixed axis is on the actual disc. The moment of inertia of a disc about its center is 1 = 0.5 M R²...Hint: Use the parallel axis theorem.AnilA mass weighing 4 pounds stretches a spring 2 feet. The system is submerged in a medium which offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s. Find the following part a and b. A) Find the equation of motion, x(t). B) What type of damped motion is this system?
- Consider the schematic of the single pendulum. M The kinetic energy T and potential energy V may be written as: T = ²m²²8² V = -gml cos (0) аас dt 80 The Lagrangian L is given by L=T-V, and the Euler-Lagrange equations for the motion of the pendulum are given by the following second order differential equation in : ас 80 = 11 = 0 Write down the second order ODE using the specific T and V defined above. Please write this ODE in the form = f(0,0). Notice that this ODE is not linear! Now you may assume that l = m = g = 1 for the remainder of the problem. You may still suspend variables to get a system of two first order (nonlinear) ODEs by writing the ODE as: w = f(0,w) What are the fixed points of this system where all derivatives are zero? Write down the linearized equations in a neighborhood of each fixed point and determine the linear stability. You may formally linearize the nonlinear ODE or you may use a small angle approximation for sin(0); the two approaches are equivalent.A spring mass system consists of a sping with spring constant k and an attached block of mass m is submerged in a liquid that produces a damping force Fr. m=2kg Fr= 18 times the instaneous velocity of the center of mass of the block k=36 n/m If the mass is initially released from rest 1 meter below equilibrium position a. Give a 2nd degree equation that describe the motion of the center of mass of the attached block b. Solve the equation in part aA horizontal spring mass system oscillates on a frictionless plane. At time t=0, it is moving left at position x=9 cm. It has velocity v=0, at positions x=0 cm and 12 cm, and completes one full cycle in 2 seconds. Write the position and velocity kinematic equations for this oscillating system, including the phase constant.
- The system in the figure below is in equilibrium, and its free body diagram drawn on the right. The distance, d is 1.14 m and each of the identical spring's relaxed length is l0 = 0.57 m. The mass, m of 0.86 kg brings the point P down to a height h = 15 cm. The mass of the springs are negligible. Calculate the following quantities: (a) The angle ? (b) The force exerted on P by the right spring (c) The force exerted on P by the left spring (d) The total spring length (e) The stretch length (f) The stiffness constant of the springsDevelop a Lagrangian for the double pendulum. You may need to make some assumptions to simplify the problem. You may also need to introduce some new variables to make the problem work. Make sure that is explained.A block of mass m = 0.52 kg attached to a spring with force constant 143 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. Refer to attached Image. (a) At that instant, find the force on the block. (b) At that instant, find its acceleration.