A door stopper spring is held at an angle from its equilibrium position and then released, and the angular velocity of the plastic end is given by the function:w(t) = 3e-0.2tcos(7t)1. Find its angular acceleration function a (t).2. Find its angular displacement function 0 (t), assuming 0 (0) = 0.3. If the rotational motion is confined to the xy plane, what is the direction of the acceleration at t-0?Justify your answers with your rationale and equations used.Edit View InsertFormat Tools Table12pt vParagraphBIUA99+upCintelCORE17田

Angular acceleration is given by ω(t) = 3e-0.2tcos(7t) 1. Angular acceleration = dω(t)dt 2. Angular…

Answered: A door stopper spring is held at an…

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter11: Dynamics Of Rigid Bodies

Section: Chapter Questions

Problem 11.7P

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A uniform rod of mass M and length L is free to swing back and forth by pivoting a distance x from its center. It undergoes harmonic oscillations by swinging back and forth under the influence of gravity.Randomized Variables M = 2.4 kgL = 1.6 mx = 0.38 m a) In terms of M, L, and x, what is the rod’s moment of inertia I about the pivot point. b) Calculate the rod’s period T in seconds for small oscillations about its pivot point. c) In terms of L, find an expression for the distance xm for which the period is a minimum.
The hoop is cast on the rough surface such that it has an angular velocity w= 5 rad/s and an angular acceleration a = 4 rad/s. Also, its center has a velocity of vo = 5 m/s and a deceleration ao = 2 m/s. Determine the magnitude of the acceleration of point Band its direction angle measured CCW from the z positive axis. 4Y 45° 0.3 m Select one OA ap - 5.04 m/s; and 0 170.31 O B.ap 6.86 m/s; and0 160.12 7.81 m/st; and 0 162.62 O D.ap 9.29 m/s and 0- 151.34
2. A disk of radius R and mass m is rolling down an inclined plane at an angle a. The coefficient of static friction between the R inclined plane and the disk is µs. The disk rolls without slipping if Hs becomes sufficiently high; however, the disk will begin to slip for µs below a certain threshold. (a) Assuming that there is no slipping, list down the Lagrangian equations of motion. Include the constraint forces at the point of contact and use the coordinate axis indicated on the figure on the right. (b) What is the value of us at which the disk would begin to slip?
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