Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 10, Problem 62P
An object moves in
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Let’s begin with a straightforward example of simple harmonic motion (SHM). A spring is mounted horizontally on an air track as in (Figure 1), with the left end held stationary. We attach a spring balance to the free end of the spring, pull toward the right, and measure the elongation. We determine that the stretching force is proportional to the displacement and that a force of 6.0 NN causes an elongation of 0.030 mm. We remove the spring balance and attach a 0.50 kgkg object to the end, pull it a distance of 0.040 mm, release it, and watch it oscillate in SHM as in (Figure 2). Find the following quantities:
The force constant of the spring
The maximum and minimum velocities attained by the vibrating object
The maximum and minimum accelerations
The velocity and acceleration when the object has moved halfway to the center from its initial position
The kinetic energy, potential energy, and total energy in the halfway position
If you had pulled the object out a distance of…
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
Ql: (Section A) Considering single degree undamped vibration system and
Newton's equation as follow: më +kx=0; find the solution of the displacement
equation [(t)=Cietwnt+C2e¬i®n'] for the case with:
Wn = 2 rad/s, x (0) = 1 mm, and x(0) = V5 mm/s.
(Section B) Given the matrix equation of motion of a two degree-of-freedom system
2k -k ||x,
= 0
-k 4k ||x2
Зт
as:
m ||*.
Determine (a) the natural frequencies, (b) the modes shapes.
Chapter 10 Solutions
Physics
Ch. 10.2 - Prob. 10.1PPCh. 10.2 - Prob. 10.2CPCh. 10.2 - Prob. 10.2PPCh. 10.3 - Stress-strain graphs for two different materials...Ch. 10.3 - Prob. 10.3PPCh. 10.4 - Prob. 10.4PPCh. 10.4 - Prob. 10.5PPCh. 10.5 - Prob. 10.5CPCh. 10.5 - Prob. 10.6PPCh. 10.6 - Prob. 10.6CP
Ch. 10.6 - Practice Problem 10.7 Energy at Maximum...Ch. 10.7 - Prob. 10.7CPCh. 10.7 - Prob. 10.8PPCh. 10.8 - Practice Problem 10.9 Pendulum on the Moon
A...Ch. 10.8 - Prob. 10.8CPCh. 10.8 - Prob. 10.10PPCh. 10 - Prob. 1CQCh. 10 - Prob. 2CQCh. 10 - Prob. 3CQCh. 10 - Prob. 4CQCh. 10 - Prob. 5CQCh. 10 - Prob. 6CQCh. 10 - Prob. 7CQCh. 10 - Prob. 8CQCh. 10 - Prob. 9CQCh. 10 - Prob. 10CQCh. 10 - Prob. 11CQCh. 10 - Prob. 12CQCh. 10 - Prob. 13CQCh. 10 - Prob. 14CQCh. 10 - Prob. 15CQCh. 10 - Prob. 16CQCh. 10 - Prob. 17CQCh. 10 - Prob. 18CQCh. 10 - Prob. 1MCQCh. 10 - Prob. 2MCQCh. 10 - Prob. 3MCQCh. 10 - Prob. 4MCQCh. 10 - Prob. 5MCQCh. 10 - Prob. 6MCQCh. 10 - Prob. 7MCQCh. 10 - Prob. 8MCQCh. 10 - Prob. 9MCQCh. 10 - Prob. 10MCQCh. 10 - Prob. 11MCQCh. 10 - Prob. 12MCQCh. 10 - Prob. 13MCQCh. 10 - Prob. 14MCQCh. 10 - Prob. 15MCQCh. 10 - Prob. 16MCQCh. 10 - Prob. 17MCQCh. 10 - Prob. 18MCQCh. 10 - Prob. 19MCQCh. 10 - Prob. 20MCQCh. 10 - 1. A steel beam is placed vertically in the...Ch. 10 - Prob. 2PCh. 10 - 3. A man with a mass of 70 kg stands on one foot....Ch. 10 - Prob. 4PCh. 10 - Prob. 5PCh. 10 - Prob. 6PCh. 10 - Prob. 7PCh. 10 - Prob. 8PCh. 10 - Prob. 9PCh. 10 - Prob. 10PCh. 10 - Prob. 11PCh. 10 - Prob. 12PCh. 10 - Prob. 13PCh. 10 - Prob. 14PCh. 10 - Prob. 16PCh. 10 - Prob. 15PCh. 10 - 17. The leg bone (femur) breaks under a...Ch. 10 - Prob. 18PCh. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 25PCh. 10 - Prob. 26PCh. 10 - Prob. 27PCh. 10 - Prob. 28PCh. 10 - Prob. 29PCh. 10 - Prob. 30PCh. 10 - Prob. 31PCh. 10 - Prob. 32PCh. 10 - Prob. 33PCh. 10 - Prob. 34PCh. 10 - Prob. 35PCh. 10 - Prob. 36PCh. 10 - Prob. 37PCh. 10 - Prob. 38PCh. 10 - Prob. 39PCh. 10 - Prob. 40PCh. 10 - Prob. 41PCh. 10 - Prob. 42PCh. 10 - Prob. 43PCh. 10 - Prob. 44PCh. 10 - Prob. 45PCh. 10 - Prob. 46PCh. 10 - Prob. 47PCh. 10 - Prob. 48PCh. 10 - Prob. 49PCh. 10 - 50. The diaphragm of a speaker has a mass of 50.0...Ch. 10 - Prob. 51PCh. 10 - Prob. 52PCh. 10 - Prob. 53PCh. 10 - Prob. 54PCh. 10 - Prob. 55PCh. 10 - Prob. 57PCh. 10 - Prob. 59PCh. 10 - 58. An object of mass 306 g is attached to the...Ch. 10 - Prob. 58PCh. 10 - Prob. 60PCh. 10 - Prob. 61PCh. 10 - An object moves in SHM. Its position as a function...Ch. 10 - Prob. 63PCh. 10 - Prob. 64PCh. 10 - Prob. 65PCh. 10 - Prob. 66PCh. 10 - Prob. 67PCh. 10 - Prob. 68PCh. 10 - Prob. 69PCh. 10 - Prob. 70PCh. 10 - Prob. 71PCh. 10 - 72. A grandfather clock is constructed so that it...Ch. 10 - Prob. 73PCh. 10 - Prob. 74PCh. 10 - Prob. 75PCh. 10 - Prob. 76PCh. 10 - Prob. 77PCh. 10 - Prob. 78PCh. 10 - Prob. 79PCh. 10 - Prob. 80PCh. 10 - Prob. 81PCh. 10 - Prob. 82PCh. 10 - Prob. 83PCh. 10 - Prob. 84PCh. 10 - Prob. 85PCh. 10 - Prob. 86PCh. 10 - Prob. 87PCh. 10 - Prob. 89PCh. 10 - Prob. 88PCh. 10 - Prob. 90PCh. 10 - Prob. 91PCh. 10 - Prob. 92PCh. 10 - Prob. 93PCh. 10 - Prob. 94PCh. 10 - Prob. 95PCh. 10 - Prob. 96PCh. 10 - Prob. 97PCh. 10 - Prob. 98PCh. 10 - Prob. 99PCh. 10 - 100. When the tension is 402 N, what is the...Ch. 10 - Prob. 101PCh. 10 - Prob. 105PCh. 10 - Prob. 103PCh. 10 - Prob. 102PCh. 10 - Prob. 104PCh. 10 - Prob. 106PCh. 10 - Prob. 107PCh. 10 - Prob. 108PCh. 10 - 109. The motion of a simple pendulum is...Ch. 10 - Prob. 110PCh. 10 - Prob. 111PCh. 10 - Prob. 112PCh. 10 - Prob. 113P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- The motion of a mass and spring is described by the following equation: 11y"+4y+6y= 35 cos(yt) Identify the value of y that would produce resonance in the system. Give an exact value, but you don't need to simplify radicals. Y What is the amplitude of the steady-state solution when the system is at resonance? Round your answer to two decimal places. The amplitude is If there was no external force, the oscillation of the spring could be described in the form A sin(ßt + p). What is the value of B? Give an exact value, but you don't need to simplify radicals. Вarrow_forwardAn object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) 8 centimeters, and then released. Write an equation for the distance d of the object from its rest position, after t seconds if the amplitude is 8 centimeters and the period is 6 seconds. The equation for the distance d of the object from its rest position is (Type an exact answer, using x as needed. Use integers or fractions for any numbers in the equation.) Enter your answer in the answer box. Save for Later 10:02 PM 4) 11/15/2020 Type here to search PgUp F11 PgDn F12 End Home F9 PrtScn DII F10 In F4 F5 F6 F7 F8 F1 F2 F3 2$ & 2 4. 5 6 7 8 E Y U P T R 3. W/arrow_forwardI need help with #7. It’s an oscillating pendulum. Use the period of oscillating pendulum equation. T = 2pi * (L/g)^0.5arrow_forward
- Considering an undamped, forced oscillator (b = 0), show that equation (1) is a solution of equation (2). (1) x = A cos(wt + ¢) d²x EF = ma → Fo sin wt – bOK – kx = m9 dt? xp dt Use an amplitude given by the following equation. (Submit a file with a maximum size of 1 MB.) Fo A V (w? - w,3)? + marrow_forwardShow that the function x(t) = A cos ω1t oscillates with a frequency ν = ω1/2π. What is the frequency of oscillation of the square of this function, y(t) = [A cos ω1t]2? Show that y(t) can also be written as y(t) = B cos ω2t + C and find the constants B, C, and ω2 in terms of A and ω1arrow_forwardA mass of 3kg stretches a spring 40cm. Suppose the mass is displaced an additional 12em in the positive (downward) direction and then ruleased. Suppose that the damping constant is 2N/m and assume g9.8 m/s is the gravitational accelaration. Set up a differential equation that describes this system. Let a to denote the displacement, in metern, of the mass from its equilbrium position, and give your answer in terms of z, , a". 3"+ 2 + 245r=0 b) Enter the intial conditions (0) 12 m. (0) o m/s is this wyotem under damped, over damped, or critically damped? under dampedarrow_forward
- A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass is slowly lifted along a circular arc to a height h. a. Assuming the only force acting on the mass is the gravitational force, show that the component of this force acting along the arc of motion is F = mg sin u. b. Noting that an element of length along the path of the pendulum is ds = L du, evaluate an integral in u to show that the work done in lifting the mass to a height h is mgh.arrow_forwardAn object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) 9 centimeters, and then released. Write an equation for the distance d of the object from its rest position, after t seconds if the amplitude is 9 centimeters and the period is 6 seconds. The equation for the distance d of the object from its rest position is (Type an exact answer, using z as needed. Use integers or fractions for any numbers in the equation.) (? Enter your answer in the answer box. Save for Later 3:18 PM O Type here to search O 11/15/2020 PgUp PgDn F12 DII PrtScn Home F9 End F10 F11 Ins F4 F5 F6 F7 F8 F1 F2 F3 2$ & ) %23 %3D 3. 4. 5 6 7 8 E R Y U | [ Tarrow_forwardA mass of 3kg stretches a spring 20cm. Suppose the mass is displaced an additional 10cm in the positive (downward) direction and then released. Suppose that the damping constant is 2 N· s/m and assume g = 9.8 m/s² is the gravitational acceleration. (a) Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x, x', x". (b) Enter the initial conditions: x(0) = m, x' (0) = m/sarrow_forward
- For a simple harmonic oscillator with x = A sin wt write down an expression for the magnitude of acceleration. Please use II * II for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate (without the quotes). For power (e.g. A) use A^2 or A*A. For trigonometric functions use the usual sin and cos, while for Greek letters such as w, use omega. Please use the "Display response" button to check you entered the answer you expect.arrow_forwardConsider a simple pendulum of length L with a mass m. Derive the angular frequency of oscillation for the pendulum when it is displaced by a small angle. Assume it is in a gravitational field with the magnitude of acceleration due to gravity equal to g. (That is, you need to find MOI and d for a simple pendulum and then use the equation for ω for a simple pendulum.)arrow_forwardThe period of motion of an object-spring system is T = 0.642 s when an object of mass m= 266 g is attached to the spring. (a) Find the frequency of motion in hertz. (b) Find the force constant of the spring. (c) If the total energy of the oscillating motion is 0.176 J, find the amplitude of the oscillations. please show every step so I can learn how to do it. Thank you!arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
SIMPLE HARMONIC MOTION (Physics Animation); Author: EarthPen;https://www.youtube.com/watch?v=XjkUcJkGd3Y;License: Standard YouTube License, CC-BY