EBK ENGINEERING MECHANICS
15th Edition
ISBN: 9780137569830
Author: HIBBELER
Publisher: VST
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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?
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Find the equation of motion of the following spring system.
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
F₂
Derive 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 system
Chapter 22 Solutions
EBK ENGINEERING MECHANICS
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
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