Problem 2.2 The nitrogen atom in an ammonia molecule can be assumed to oscillate in simple harmonic motion, so that its position at any time t is given by z = A cos wt, where A and are constants. Obtain expressions for its velocity and acceleration as functions of time.

Problem 2.2 The nitrogen atom in an ammonia molecule can be assumed to oscillate in simple harmonic motion, so that its position at any time t is given by z = A cos wt, where A and are constants. Obtain expressions for its velocity and acceleration as functions of time.

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

A potential difference of 81 mV exists between the inner and outer surfaces of a cell membrane. The inner surface is negative relative to the outer surface. How much work is required to eject a positive sodium ion (Na+) from the interior of the cell?_______________________J
I am having a hard time finding the meaning of what T2 is in the equation. Do I just square the T or do something else? Thanks for the help in advanced.
Solve for question 3 The θ integration fails if α is non-constant. There is also a type of situation where the step before the integration fails, involving ω. Question 1: derive ω = αt + ω0. Start with the derivatives I began with, and derive this equation. Question 2: derive θ = 1/2αt2 + ω0t + θ0. You may use prior derived results. Question 3: derive θ = θ0 + (ω + ω0) t/2. You probably need to use prior derived results.
PART A k = 2.000 N/m M=0.125kg %3D A 0.125kg mass is attached to a horizontal spring of spring constant k = 2 N/m and set into oscillation. Assume frictionless floor. What is the angular frequency o of the vibration? o = How about the vibrating frequency f in Hz? f = The position of the mass is given as x = A cos (ot + o). With your calculated value of w, fill in the following table (don't forget to set your calculator to "radian mode"). Each row represents a different oscillation with the same spring, pay attention to sign: А (m) x (m) v (m/s) a (m/s?) t (s) фо (rad) F (N) 0.03 2.5 0.3 0.04 0.02 0.2 0.06 0.1 0.4 0.04 0.3 -0.2 0.5 0.04 0.1 0.1
Problem 2.6 The position of a particle is given by r = 2t (meters), 0 = 5t (radians). (a) Plot the path of the particle. (b) Obtain an expression for the speed as a function of time. Answers: (a) This is the spiral of Archimedes. (b) v = (4+100t?)1/2 m/s.
Problem 4.6 Obtain the equations of motion for a spherical pendulum, that is, a pendulum that is not constrained to oscillate in a plane.
Problem 4.19 A bead slides down a wire. You want to determine the shape the wire must have for the bead to slide from its initial position to its final position in the least amount of time. (This is called the "brachistochrone" problem.) Note that the quantity to be minimized is the time and that dt = ds/v where the velocity v is given by conservation of energy. I do not expect you to actually solve this problem; it will be sufficient if you write the functional that describes the system.12