y = yo cos wt l φ m A pendulum has a mass m connected by a rigid rod of length to a pivot point. An external force causes the pivot point to oscillate vertically, with y yo cos wt. Gravity is pointing downward. = a) [10 pts] Write the Lagrangian for the pendulum, in terms of the angular coordinate o.

y = yo cos wt l φ m A pendulum has a mass m connected by a rigid rod of length to a pivot point. An external force causes the pivot point to oscillate vertically, with y yo cos wt. Gravity is pointing downward. = a) [10 pts] Write the Lagrangian for the pendulum, in terms of the angular coordinate o.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Need help on this question. The anwser should be 2.07
Fill in each blank so that the resulting statement is true.
O mr - 2mrre- mgr sin e wU A simple pendulum of length b and bob with mass m is attached to massless support moving vertically with constant acceleration a. The Lagrangian of the system is Select one: OL-m(a*e - 2atblcond + b") + OL-m(a* - 2atbésind + b0") + mgbaino OL=m(a* + 2atbbsind + P0) + mg(b cos-at") OL- m(a*t - 2atbdcose + 6*0) + mg(b sind-at"). zed coordinates you need to describe this system
straight line is always acted upon by a force from the centre of the path and directed Ex. 2: A particle of mass 8 gm moving in a and maximum acceleration, if the amplitude is towards the centre. Find its maximum velocity sse magnitude is 128 times the displacement 5 cm.
It is known that a general solution for the position of a harmonic oscillator is x(t) = C cos (wt) + S sin (wt), where C, S, and ware constants. (Figure 2) Your task, therefore, is to determine the values of C, S, and w in terms of k, m,and init and then use the connection between x (t) and a (t) to find the acceleration. Figure L min x=0 Xinit 1 of 2 > Part A Combine Newton's 2nd law and Hooke's law for a spring to find the acceleration of the block a (t) as a function of time. Express your answer in terms of k, m, and the coordinate of the block x (t). ► View Available Hint(s) a (t) = Submit 17 ΑΣΦ Part B Complete previous part(s) Review | Constants ?
If you did the previous question right, you hopefully got an expression for yo. You may notice that you can simplify the differential equation a little bit: d'y k (y – yo) dt2 т The parameter yo now plays the roll of the "relaxed length". A better term may be "equilibrium value for y". But mathematically, it's identical to a relaxed length with the spring as the only force. We continue using this equation: y(t) = Y0 + A cos(wt + y) Now, solve for A (in cm) with these parameters. Again, if you need more information, enter -100000. The parameters are: •m = 200 grams • Yo = (equilibrium value) = 40 cm • k = (spring constant) = 0.03 N/cm
i need the answer quickly
need asap please
Two blocks and three springs are Configured below. All motion is honzental. when the blocks are aū jest spoings are unstretched: Kz k3 Suppse mi=2m mzzm, K,=4k okzz k, Ksz 2k. Find the charactesistics freguencies Foo Small oscillations.
DONT MIND THE BIG NUMBER ON THE RIGHT, IT IS JUST FOR NUMBERING. MAKE SURE IT IS CORRECT AND TYPEWRITTEN TO GET AN UPVOTE. NO UPVOTE IF IT IS HANDWRITTEN. THANK YOU
A double pendulum has two degrees of freedom. Produce a reasonable Lagrangian L(01, 02, 01, 02) for describing a double pendulum free to move in a plane in gravity g? Assume the connecting rods are rigid. 4₁ m₁ L₂ m₂²₂ Hint: Let's just assume L₁ 2 2 L = ¼m²³² (0₂² +401² +30₁02 cos(0₁ - 0₂)) + ½ mgl (3 cos 0₁ + cos 0₂). L₂ = 1 and that m₁ = m₂ = m and show that the Lagrangian reduces to :
Consider a square sheet with sides: a. The sheet behaves like a compund pendulum and oscillates around an axis from one of the corners of the sheet where its Perpendicular to it. Find the period of the pandelum.