Question

Notify Me Bookmark

Let be given a mathematical pendulum (Fig. 1) with mass m = 786 g, length l = 250 mm and angle φ as degree of freedom. The weight force FG acts on the mass, friction effects can be neglected. Figure 1: Mathematical pendulum [3]. (i) Set up the equation of motion with the angle φ as the system variable.

Let be given a mathematical pendulum (Fig. 1) with mass m = 786 g, length l = 250 mm and angle φ as degree of freedom. The weight force FG acts on the mass, friction effects can be neglected. Figure 1: Mathematical pendulum [3]. (i) Set up the equation of motion with the angle φ as the system variable.

Image text
Let be given a mathematical pendulum (Fig. 1) with mass m = 786 g , length l = 250 m m and angle φ as degree of freedom. The weight force F G acts on the mass, friction effects can be neglected. Figure 1: Mathematical pendulum [ 3 ] . (i) Set up the equation of motion with the angle φ as the system variable.

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

A block of mass m slides on a frictionless wedge that makes an angle of π/4 to the horizontal. The wedge, with mass M, sits on a frictionless horizontal surface and is connected to a fixed point by a horizontal spring with force constant k and unstretched length a. Analyse this system in a similar manner to lectures, to answer the following: (a) Write the Lagranian for this system. (b) Use the Lagrangian to derive equations of motion for the block and the wedge. (c) Show that the wedge undergoes simple harmonic motion, with an angular frequency that can be written ω = k M + m(1 − 1 2)
Solution
0 0

The truck with a ladder plotted in Fig. 5 starts from rest (and accelerates to the left) with an acceleration of 7 m/s2. The ladder of mass m = 10 kg, which is the rigid body of interest in this problem, can be modeled as a uniform slender rod that is hinged at point A and supported at point B. As a consequence, the center of mass G of the ladder is located at the midpoint of the rod. Any friction in this problem is supposed to be small enough to be neglected. a) Determine the minimum linear acceleration amin of the truck such that the ladder loses contact at point B, i. e. the normal force NB at B vanishes, and starts to rotate about point A. Do so by determining the sum of the moments about point A, and verify that for the given acceleration of the truck, the ladder will in fact lose contact at point B. b) Determine the mass moment of inertia I¯ of the ladder associated with its center of mass G. c) Use the result found in Part b) and employ the concept of relative acceleration expressed in terms of a normal-tangential coordinate system to determine the initial angular acceleration vector α of the ladder. Figure 5: A truck with a ladder accelerating from rest to the left and measurements.
Solution
0 0

Figure 6 shows a boy sitting on a swing and being pumped (pushed) by a harmonic force Fosin⁡ωt where Fo is the force amplitude and ω is the angular frequency of pumping in the horizontal direction. This forced oscillation can be modelled by a simple pendulum which consists of a lumped mass m swinging at a distance L from the pivot. (i) Write the equation of motion for this pendulum under forced vibration. (ii) Find the amplitude of angular swing based on the assumption of a small angle. (7 marks) Figure 6
Solution
0 0