PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 22, Problem 41P
If the block-and-spring model is subjected to the periodic force F=F0 cos ωt, show that the differential equation of motion is ẍ + (k/m)x = (F0/m) cos ωt , where x is measured from the equilibrium position of the block. What is the general solution of this equation?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
I
Draw the free-body diagrams and write the differential equations of motion for
the two masses in terms of x₁ and .x2.
b. Find x₁, and X20, the constant displacements of the masses caused by the gravita-
tional forces when fa(t) = 0 and when the system is in static equilibrium.
K₁
Rewrite the system equations in terms of z₁ and 22, the relative displacements of
the masses with respect to the static-equilibrium positions found in part (b).
K₂
ele
M₂
fa(1)
M₁
IIL
B
Figure P2.15
111
ele
///
K
M₁
000
M₂
K
(
000
K
fa(1)
Figure P2.16
2.16. Repeat all three parts of Problem 2.15 for the system shown in Figure P2.16. Each of
the three springs has the same spring constant K.
Determine the equivalent
torsional spring constant of a
spring that will represent the
system such that this torsional
spring will be located at where
the given bar turns. k=5N/m
and l=1.5meters (answer in N-
m) *
4 =
k = k
kz = 2k
k3 = 3k
F x
len
Determine the equivalent torsional spring constant of a spring that will represent the system such that this torsional spring will be located at where the given bar turns. k=5N/m and l=1.5meters (answer in N-m)
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
- Consider a mass-spring system shown below. X1 m k₁ ooooo The system model is given by d²x m m₁ 1 d1² dx, 2 di² 1 · + (k₁₂ + k₂) x ₂ −k ₂x₂=F₁ (1) 1 k₂ ooooo F₁ k₂x₂ + (k₂ + k ₂) x₂ = F₂(t) k₂ +k z 2 m_s (m_s²³ + k₁+k₂ ²+k₁ + k ₂ ) ( m ₂s ² + k₂ + k ₂) -k 2 where F₁(t) and F₂(t) are the inputs to the system. Find the transfer function X₁(s)/F₁(s). k ₂ (m₁s²+k₁+k₂) (m₂s² + k ₂2 +k₂ ) − k²/ 2 ₁s² + k ₁+k₂) 1 (m₂x²+₁+k₂) (m₂x²+k₂+^₂)=R} 2 ) ( m²₂ s² + k₂ + k ₂ 1 2 m₂ k ₁+k₂ 1 (m₁s²+k₁ + k₂) (m₂s² + k₂ + k 3) − k ²/ k 3 (m₂x²+k₂+k₂) (m₂x²+k₂+k₂) −R} k ² (m₂s² + k ₂+k₂) (m₂x²+k₂ +k₂) (m₂x²+k₂+A₂)-R² 3) k3 ooooo F₂arrow_forwardDerive the equation of motion of the system shown in the figure below, using the Newton's second law of motion. k1 k2 m Linear mass-spring systemarrow_forwardConsider the following equation of motion that describes the dynamics of a particle subjected to a gravitational field and restricted to the surface of a cone i +rở² sin (a)² + g cos (a) sin (a) Using the equation of motion, determine the dynamics for small oscillations around the equilibrium point. Consider that ở = . Specify the frequency of oscillation, the balance point and its stability. mr²arrow_forward
- The 10 N cylinder moves in a frictionless pipe. Spring constants are k1 = 150 N / m and k2 = 200 N / m. When the system is at rest, d = 0.5 m. (d is the distance from the right end of the arc k2). The system rotates around a fixed z-axis. Find the constant velocity of the cylinder for d = 0.20 m?arrow_forwarde(+) 3r S.E.P. The homogeneous disc with a mass of 4m and radius of 3r is supported at point 0. For small oscillations, find the equations of motion of the two – degree – of – freedom system in terms of the given parameters (k,m,r), and show them in the matrix form. The system is in the static equilibrium position at the instant given. 4m 3 2k Sm Ta(+) 5k Зт wwarrow_forwardSHOW YOUR STEP BY STEP SOLUTION. 1. Assuming that the displacement (x) resulting from the application of a force F at a point A is small, find the equivalent spring constant of the system that relates the applied force F to the displacement x. k- 2karrow_forward
- Determine the equivalent torsional spring constant of the system that will be located in the position of point 0. k=1.5N/m. The bar is 2 meters long. (answer in N-m)arrow_forwardWhich of the following cannot be the position of the mass of a mass-spring system: Ox (t) = 5.5 cos 8t O x (t) = 5 e 2t cos 7t Ox (t) = 1.25 sin(11t+2) Ox (t) = 3 cos 2t + 7 sin 2tarrow_forwardDetermine the equivalent spring stiffness of the system using the displacement of the block as the generalized coordinate E = 200 x 10" N/m2 I = 1.6 x 10°m* 6 x 10 N/m 3 m- 2 x 10° N/m m 3 x 10' N/m 5 x 10° N/marrow_forward
- The following mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x, '(0) = x2'(0) = 0) in its equilibrium position (x, (0) = x2(0) = 0) with the given external forces F, (t) = 0 and F, (t) = 270 cos 4t acting on the masses m, and m,, respectively. Find the resulting motion of the system and describe it as a %3D superposition of oscillations at three different frequencies. k2 mi ww m2 k3 - (k, + k2) k2 K= k2 - (k2 + k3) m, = 1, m, = 2; k, = 1, k, = 6, k3 = 2 %3D Find the resulting motion of the system. X4 (t) = X2(t) (Type exact answers, using radicals as needed.)arrow_forwardThe following mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x1′(0)=x2′(0)=0)in its equilibrium position (x1'(0)=x2'(0)=0) with the given external forces F1(t)=0and F2(t)=540 cos 4t acting on the masses m1and m2,respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies. m1 m2 k1 k2 k3 x1 x2 K= −k1+k2 k2 k2 −k2+k3 m1=1, m2=2; k1=1, k2=2, k3=2 Find the resulting motion of the system. x1(t) = x2(t) = (Type exact answers, using radicals as needed.)arrow_forwardGears B and D are attached to a shaft which is supported by bearings at A and C if the diameters of the gears are 12 and 6 cm respectively, radial and tangential forces act on them as shown, neglecting the weight of the gears. gears as well as the friction of the bearings, if we know that the system is rotating with a constant angular velocity. Calculate the static equilibrium of the system X Z A 175 N 12 CM 110 N B C 40 cm 6 CM D 200 N 450 N 30 cm 20 cmarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L
International Edition---engineering Mechanics: St...
Mechanical Engineering
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:CENGAGE L
Ch 2 - 2.2.2 Forced Undamped Oscillation; Author: Benjamin Drew;https://www.youtube.com/watch?v=6Tb7Rx-bCWE;License: Standard youtube license