PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 22, Problem 16P
To determine
The equivalent stiffness of a single spring with the same oscillation characteristics and the period of oscillation for each case.
(a) parallel to each other
(b) as a series
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Two identical spring-mass systems A and B are coupled by a weak middle spring
having a spring constant smaller by a factor of 100 (i.e. 100kmiddle = kA = kB).
Mass A is pulled by a small distance and released from rest, while mass B is
released from rest at its equilibrium position, at t = 0. Calculate the approximate
number of oscillations completed by mass A before its oscillations die down first.
A uniform plank of mass 2.29kg and length 39.6 cm is pivoted at one end, and the opposite end is attached to a spring of force constant 454N/m. The height of the pivot has been adjusted so that the plank will be in equilibrium when it is horizontally oriented as in the figure. Find the period of small oscillation about the equilibrium point. Answer in units of s.
8. A spring of 21 cm length reaches 30.8 cm after hanging a mass of 1/4 kilogram on it. The medium through which
the mass moves provides a damping force equal to three times the instantaneous velocity. Find the equation of
motion if the mass is released from the equilibrium position with a downward velocity of 2 m/s. Calculate the time
at which the mass reaches its extreme displacement, and what is the position of the mass at that moment? (Use
g = 9.8 m/s²)
Sol.
Chapter 22 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 22 - A spring is stretched 175 mm by an 8-kg block. If...Ch. 22 - A spring has a stiffness of 800 N/m. If a 2-kg...Ch. 22 - Prob. 3PCh. 22 - Prob. 4PCh. 22 - Prob. 5PCh. 22 - Prob. 6PCh. 22 - Prob. 7PCh. 22 - Prob. 8PCh. 22 - A 3-kg block is suspended from a spring having a...Ch. 22 - Prob. 10P
Ch. 22 - Prob. 13PCh. 22 - Prob. 14PCh. 22 - Prob. 16PCh. 22 - Prob. 17PCh. 22 - A uniform board is supported on two wheels which...Ch. 22 - Prob. 24PCh. 22 - Prob. 30PCh. 22 - Prob. 31PCh. 22 - Prob. 32PCh. 22 - Determine the differential equation of motion of...Ch. 22 - Prob. 36PCh. 22 - If the block-and-spring model is subjected to the...Ch. 22 - A block which has a mass m is suspended from a...Ch. 22 - A 4-lb weight is attached to a spring having a...Ch. 22 - A 4-kg block is suspended from a spring that has a...Ch. 22 - A 5-kg block is suspended from a spring having a...Ch. 22 - Prob. 48PCh. 22 - The light elastic rod supports a 4-kg sphere. When...Ch. 22 - Find the differential equation for small...Ch. 22 - Prob. 52PCh. 22 - The fan has a mass of 25 kg and is fixed to the...Ch. 22 - In Prob. 22-53 , determine the amplitude of...Ch. 22 - Prob. 55PCh. 22 - Prob. 56PCh. 22 - Prob. 57PCh. 22 - Prob. 58PCh. 22 - Prob. 59PCh. 22 - Prob. 60PCh. 22 - Prob. 61PCh. 22 - Prob. 62PCh. 22 - Prob. 65PCh. 22 - Determine the magnification factor of the block,...Ch. 22 - Prob. 67PCh. 22 - The 200-lb electric motor is fastened to the...Ch. 22 - Prob. 70PCh. 22 - Prob. 72PCh. 22 - Prob. 73PCh. 22 - Prob. 74PCh. 22 - Prob. 75PCh. 22 - Prob. 76PCh. 22 - Prob. 79P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- 1. A machine component of mass 0.77 kg moves with SHM in a straight line and completes 175 oscillations per minute. Find the accelerating force when the component is 50 mm from mid-travel.arrow_forward2. A closed coiled helical spring has a stiffness of 1400 N/m.If a 10kg mass is attached to the end of the spring,calculate the periodic time and the frequency of oscillation when the spring vibrates vertically.arrow_forward1. A uniform rod of mass m is supported by a pin at 0 and spring of constant k and is connected to a dashpot of damping coefficient c. Determine the differential equation of the motionfor small oscillations in terms of m, k. c and L What would be the natural period of this system for small oscillations. when it is undamped. if L is 1.2 m. k is 100 N/m. and m is 3 kg? Hint: mass moment of lInertia of the rod is (mL)/12 with respect to the axis passing through its mass center. Parallel axis theorem states Ie=l, +m d² where d is the distance between the axes x and x. Spring force is k times the displacement, damping force is the c times the speed in dashpot. linear spring spring coefficient = k mass of rod m L/2 L/2 damper damping coeffient = earrow_forward
- By what factor does the amplitude change in one period of these damped oscillations?arrow_forwardAn object of mass 2 kg is attached to a spring of stiffness 200 N / m on a horizontal frictionless surface . Then it is extend by 10 cm and then let free to oscillate . 1- How long will it take to make one complete oscillation ? 2- Determine the amplitude and give an expression for the displacement as a function of time . 3- Calculate its displacement , velocity , acceleration and force acting on it after sec . 4- Calculate its velocity by the time it is extended by 0.5 cmarrow_forwardA block of mass m hangs from a spring with a spring constant k. The block is initially held so that the spring is unstretched. If the natural circular frequency of the system is 10 radians/sec, how many cycles of vibration will the block experience in five seconds after it is released?arrow_forward
- A rigid and weightless rod is restricted to oscillations in the vertical plane as shown in the figure below.Determine the natural frequency of the system of mass m.arrow_forwardA body vibrating with viscous damping makes five complete oscillations per second, and in 10 cycles its amplitude diminishes by 1/5 of the orginal value. Determine the logarithmic decrement and the damping ratio.arrow_forwardA mass attached to the end of a cantilever beam is subjected to an impulse of 5 Ns, in a direction normal to the axis of the beam and is set in oscillations. If the mass m = 700 kg, the damping ratio, length, and Young's modulus E are respectively 0.3, 3 m, and 7x 1010 N/m2, find the approximate peak response of the mass. The moment of inertia of the beam is 0.6 m4.arrow_forward
- A thin cylindrical rod of uniform mass m and length L is suspended from the ends by two massless springs with constants k1 and k2 (Distance L1 and L2 on either side of the center of mass of the rod). The motion of the center of mass is constrained to move up and down parallel to the vertical y-axis. It also experiences rotational oscillations around an axis perpendicular to the rod and passing through the center of mass (I is the moment of inertia with respect to said axis). be y1 and y2 the displacements of the two ends from their equilibrium positions, as shown in Fig. a) Find the motion's equation (consider k1=k2=k)arrow_forward3.32. A single degree of freedom mass-spring system has a mass m=9 kg, a spring stiffness coefficient k = 8 x 10° N/m, a coefficient of dry friction u = 0.15, an initial displacement xo = 0.02 m, and an initial velocity io = 0. Determine the number of cycles of oscillations of the mass before it comes to rest.arrow_forward3. A helical spring with a mass of 6kg has a mass of 10kg attached to its free end. The : released. If the mass is now pulled down 40mm from the equilibrium position and spring stiffness is 532N/m find the frequency of oscillation.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Ch 2 - 2.2.2 Forced Undamped Oscillation; Author: Benjamin Drew;https://www.youtube.com/watch?v=6Tb7Rx-bCWE;License: Standard youtube license