Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 11.3, Problem 14P
To determine
The stiffness of spring
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100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph
for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Produce an animation of the system for all solutions for the first minute.
Chapter 11 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 11.3 - Determine the required magnitude of force P to...Ch. 11.3 - Determine the magnitude of force P required to...Ch. 11.3 - The linkage is subjected to a force P = 2 kN....Ch. 11.3 - Prob. 4FPCh. 11.3 - Determine the angle where the 50-kg bar is in...Ch. 11.3 - Prob. 6FPCh. 11.3 - Use the method of virtual work to determine the...Ch. 11.3 - The scissors jack supports a load P. Determine the...Ch. 11.3 - If a force of P = 5 lb is applied to the handle of...Ch. 11.3 - Prob. 4P
Ch. 11.3 - Prob. 5PCh. 11.3 - Prob. 6PCh. 11.3 - When = 20, the 50-lb uniform block compresses the...Ch. 11.3 - Prob. 8PCh. 11.3 - The 4-ft members of the mechanism are pin...Ch. 11.3 - The thin rod of weight W rests against the smooth...Ch. 11.3 - If each of the three links of the mechanism have a...Ch. 11.3 - Prob. 12PCh. 11.3 - Prob. 13PCh. 11.3 - Prob. 14PCh. 11.3 - Prob. 15PCh. 11.3 - Prob. 16PCh. 11.3 - When = 30, the 25-kg uniform block compresses the...Ch. 11.3 - Prob. 18PCh. 11.3 - The Nuremberg scissors is subjected to a...Ch. 11.3 - The crankshaft is subjected to a torque of M = N ...Ch. 11.3 - Prob. 21PCh. 11.3 - The spring is unstretched when = 0. If P = 8 lb,...Ch. 11.3 - Prob. 23PCh. 11.3 - Prob. 24PCh. 11.3 - The dumpster has a weight W and a center of at...Ch. 11.7 - The potential energy of a one-degree-of-freedom...Ch. 11.7 - Prob. 27PCh. 11.7 - Prob. 28PCh. 11.7 - Prob. 29PCh. 11.7 - Prob. 30PCh. 11.7 - Prob. 31PCh. 11.7 - Prob. 32PCh. 11.7 - The uniform bar has a mass of 80 Kg. Determine the...Ch. 11.7 - The uniform bar AD has a mass of 20kg. If the...Ch. 11.7 - Prob. 35PCh. 11.7 - Prob. 36PCh. 11.7 - Determine me angle for equilibrium and...Ch. 11.7 - Prob. 38PCh. 11.7 - Prob. 39PCh. 11.7 - Prob. 40PCh. 11.7 - The uniform rod has a mass of 100 kg. If the...Ch. 11.7 - Prob. 42PCh. 11.7 - The buck has a mass of 20 Mg and a mass center at...Ch. 11.7 - Prob. 44PCh. 11.7 - Prob. 45PCh. 11.7 - Prob. 46PCh. 11.7 - Prob. 47PCh. 11.7 - Prob. 48PCh. 11.7 - Prob. 49PCh. 11.7 - Prob. 1RPCh. 11.7 - Prob. 2RPCh. 11.7 - The punch press consists of the ram R, connecting...Ch. 11.7 - Prob. 4RPCh. 11.7 - Prob. 5RPCh. 11.7 - Prob. 6RPCh. 11.7 - The uniform bar AB weighs 100 lb. If both spring...Ch. 11.7 - The spring attached to the mechanism has an...
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