Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 9.5, Problem 5P
Find the equation of motion of a particle moving along the
(This is a simple harmonic oscillator.)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
This problem is an example of critically damped harmonic motion.
A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring
feet. The ball is started in motion from the equilibrium position with a downward velocity of 5
feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times
its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest
position. Find y in terms of t.
Take as the gravitational acceleration 32 feet per second per second. (Note that the positive y
direction is down in this problem.)
y =
le
charge Q acts as a point charge to create an electric field.Its strength, measured a distance of 30 cm away, is 40 N/C.What is the magnitude of the electric field strength that you think you would expect to be measured at a distance of 60 cm away?
Please give me answer very fast in 5 min sini
Chapter 9 Solutions
Mathematical Methods in the Physical Sciences
Ch. 9.1 - The speed of light in a medium of index of...Ch. 9.1 - The speed of light in a medium of index of...Ch. 9.1 - The speed of light in a medium of index of...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...
Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Find the geodesics on a plane using polar...Ch. 9.3 - Prob. 16PCh. 9.3 - Find the geodesics on the cone x2+y2=z2. Hint: Use...Ch. 9.3 - Find the geodesics on a sphere. Hints: Use...Ch. 9.4 - Verify equations (4.2).Ch. 9.4 - Show, in Figure 4.4, that for a point like...Ch. 9.4 - In the brachistochrone problem, show that if the...Ch. 9.4 - Consider a rapid transit system consisting of...Ch. 9.4 - In Problems 5 to 7, use Fermats principle to find...Ch. 9.4 - In Problems 5 to 7, use Fermats principle to find...Ch. 9.4 - In Problems 5 to 7, use Fermats principle to find...Ch. 9.5 - (a) Consider the case of two dependent variables....Ch. 9.5 - Set up Lagranges equations in cylindrical...Ch. 9.5 - Do Problem 2 in spherical coordinates.Ch. 9.5 - Use Lagranges equations to find the equation of...Ch. 9.5 - Find the equation of motion of a particle moving...Ch. 9.5 - A particle moves on the surface of a sphere of...Ch. 9.5 - Prove that a particle constrained to stay on a...Ch. 9.5 - Two particles each of mass m are connected by an...Ch. 9.5 - A mass m moves without friction on the surface of...Ch. 9.5 - Do Example 3 above, using cylindrical coordinates...Ch. 9.5 - A yo-yo (as shown) falls under gravity. Assume...Ch. 9.5 - Find the Lagrangian and Lagranges equations for a...Ch. 9.5 - A particle moves without friction under gravity on...Ch. 9.5 - 2A hoop of mass M and radius a rolls without...Ch. 9.5 - Generalize Problem 14 to any mass M of circular...Ch. 9.5 - Find the Lagrangian and the Lagrange equation for...Ch. 9.5 - A simple pendulum (Problem 4) is suspended from a...Ch. 9.5 - A hoop of mass m in a vertical plane rests on a...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.6 - In Problems 1 and 2, given the length l of a curve...Ch. 9.6 - In Problems 1 and 2, given the length l of a curve...Ch. 9.6 - Given 10 cc of lead, find how to form it into a...Ch. 9.6 - Prob. 4PCh. 9.6 - A curve y=y(x), joining two points x1 and x2 on...Ch. 9.6 - In Problem 5, given the volume, find the shape of...Ch. 9.6 - Integrate (6.2), simplify the result and integrate...Ch. 9.8 - (a) In Section 3, we showed how to obtain a first...Ch. 9.8 - Find a first integral of the Euler equation to...Ch. 9.8 - Find a first integral of the Euler equation to...Ch. 9.8 - Find a first integral of the Euler equation to...Ch. 9.8 - Write and solve the Euler equations to make...Ch. 9.8 - Write and solve the Euler equations to make...Ch. 9.8 - Write and solve the Euler equations to make...Ch. 9.8 - Find the geodesics on the cylinder r=1+cos.Ch. 9.8 - Prob. 9MPCh. 9.8 - Find the geodesics on the parabolic cylinder y=x2.Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - Find Lagranges equations in polar coordinates for...Ch. 9.8 - Repeat Problem 19 if V=K/r.Ch. 9.8 - Write Lagranges equations in cylindrical...Ch. 9.8 - In spherical coordinates, find the Lagrange...Ch. 9.8 - A particle slides without friction around a...Ch. 9.8 - Write and simplify the Euler equation to make...Ch. 9.8 - Prob. 25MPCh. 9.8 - A wire carrying a uniform distribution of positive...Ch. 9.8 - Find a first integral of the Euler equation for...Ch. 9.8 - Write the Lagrange equation for a particle moving...
Additional Math Textbook Solutions
Find more solutions based on key concepts
For the following exercises, consider an athlete running a 40-m dash. The position of the athlete is given by d...
Calculus Volume 1
CHECK POINT 1 In a survey on musical tastes, respondents were asked: Do you listed to classical music? Do you l...
Thinking Mathematically (6th Edition)
Why do we not talk about a greatest common multiple and a least common factor?
Mathematics for Elementary Teachers with Activities (5th Edition)
Solve each problem involving proportions. Price of Gasoline If 6 gallons of premium unleaded gasoline cost $17....
Mathematical Ideas (13th Edition) - Standalone book
The table by using the given graph of h.
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
If R is the event that a convict committed armed robbery and D is the event that the convict pushed dope, state...
Probability and Statistics for Engineers and Scientists
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- A tank contains 220 gallons of water and 50 oz of salt. Water containing a salt concentration of 1/8(1+1/2sint) oz/gal flows into the tank at a rate of 5 gal/min, and the mixture in the tank flows out at the same rate. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation?arrow_forwardEnter the equation of the function cos(x) that has a vertical shift of 4 units up, and a phase shift of π6 units right.arrow_forwardCompare the phase shift and amplitude of y=-cos(x-180∘) and y=-2sin(x-90∘). Which of the following choices is the correct comparison? a The cosine function has a phase shift that is 12 that of the sine function and in the same direction; the amplitude of the cosine function is 2 times that of the sine function. b The cosine function has a phase shift that is 12 that of the sine function and in the opposite direction; the amplitude of the cosine function is 12 that of the sine function. c The cosine function has a phase shift that is 2 times larger than the phase shift of the sine function and in the same direction; the amplitude of the cosine function is 12 that of the sine function. d The cosine function has a phase shift that is 2 times larger than that of the sine function and in the opposite direction; the amplitude of the cosine function is 2 times that of the sine function.arrow_forward
- Please walk me through this problem. Thank you!arrow_forwardThe number of hours of daylight each day for a particular city can be modeled using the sinusoidal function s(m)=5sin(2π/12m−π/2)+13 , where s is the number of hours of sunlight per day, and m represents the month of the year, with m=1 corresponding to January, m=2 corresponding to February, etc. What is the number of hours of daylight in the longest day of the year? A.8 hours B. 13 hours C.18 Hours D.24 hoursarrow_forward(cos(3æ)(/1 – cos(5æ))dæ - Solve Now Feedbackarrow_forward
- An object is moving on a straight line according to the following position function. (a) The velocity and the acceleration of this displacement are v(t) = a(t)= x(t) = = -9 cos(5t) - 9√/3 sin(5t) meters (b) This position is in simple harmonic motion since (c) We rewrite x (t) as A cos(wt + o). A = a(t) = == W3 (d) Find the amplitude, the period and the frequency of (t). Amplitude = meters. Period= ² x (t) seconds. Frequency= m/s m/s2 1/seconds.arrow_forwardA Ferris wheel has a radius of 28 m. Its center is 29 m above the ground. It rotates once every 24 s. Suppose you get on the bottom at t = 0. Write an equation that expresses your height as a function of elapsed time. oh = 28 cos T- 24 (t – 12) + 29 oh = 29 cos 27- 24 (t – 12)] + 28 h = 29 cos T- 24 (t – 12)* + 28 oh = 28 cos 27- 24 (t – 12) + 29arrow_forwardA mass weighing 16 pounds is attached to a spring whose spring constant is 25 Ib/ft. Find the equation of motion. (Use g = 32 ft/s2 for the acceleration due to gravity. Assume t is measured in seconds.) c,cos(5v7 )1+ c,sin (5v2 )t x(t) = What is the period of simple harmonic motion (in seconds)?arrow_forward
- A mass-spring system obeys simple harmonic motion according to the function f(t) = 2 cos (). Blank 1: Find the amplitude of the motion. Blank 2: Find the frequency of the motion.arrow_forwardWhat is the phase shift of this function? y=sin(3x-15pi)arrow_forwardSHOW YOUR COMPLETE SOLUTION AND GIVE WHAT IS ASKED. Apply Newton’s method to find the root(s) of the function: f(x) = (8)x 3 – (8)x 2 – (8)x + 1 = 0. The answers should begiven in a range from a = -2 to b = +2. Your iteration should stop when it reaches the change insign (polarity) in your computation. The starting point should be (a) 0.3 and (b) 0.7. Choose your own incrementvalue.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Find the solutions to a trig equation between 0 and 2pi; Author: Brian McLogan;https://www.youtube.com/watch?v=h7trDHjKCYc;License: Standard YouTube License, CC-BY