EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 9780100254961
Author: Palm
Publisher: YUZU
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Chapter 1, Problem 1.21P
Obtain a linear approximation of the function
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An object attached to a spring undergoes simple harmonic motion modeled by the differential equation
d²x
=
0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the
mass of the object, and k is the spring constant. A mass of 3 kilograms stretches the spring 0.2 meters.
dt²
Use this information to find the spring constant. (Use g = 9.8 meters/second²)
m
k
=
+ kx
The previous mass is detached from the spring and a mass of 17 kilograms is attached. This mass is
displaced 0.45 meters below equilibrium and then launched with an initial velocity of 2 meters/second.
Write the equation of motion in the form x(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants
in your equation.
x(t) =
Rewrite the equation of motion in the form ä(t) = A sin(wt + ), where 0 ≤ ¢ < 2π. Do not leave
unknown constants in your equation.
x(t) =
A higher-order differential
equation given as y" + p(x)y'
g (x)y = O is a homogenous
equation, even if p(x) = 0. A
higher-order differential equation given as y" + p(x)y' + q(x)y = 0 is
also a homogenous equation,
even if g(x) = 0.
O Only first statement is true.
O Only second statement is true.
O Both first and second statements are
true.
O Both first and second statements are
false.
Equation of motion of a suspension system is given as: Mä(t) + Cx(t) + ax² (t) + bx(t) = F(t), where
the spring force is given with a non-linear function as K(x) = ax²(t) + bx(t).
%3D
a. Find the linearized equation of motion of the system for the motion that it makes around steady state
equilibrium point x, under the effect of constant F, force.
b. Find the natural frequency and damping ratio of the linearized system. -
c. Find the step response of the system (
Numerical values: a=2, b=5, M=1kg, C=3Ns/m, Fo=1N, xo=0.05m
Chapter 1 Solutions
EBK SYSTEM DYNAMICS
Ch. 1 - Prob. 1.1PCh. 1 - Folklore has it that Sir Isaac Newton formulated...Ch. 1 - A ball is thrown a distance of 50 feet. 5 inches....Ch. 1 - An American football field is 100 yards long. How...Ch. 1 - How long is a 100-meter dash in feet?Ch. 1 - Convert 50 feet per second to miles per hour.Ch. 1 - The speed limit in some countries is 100...Ch. 1 - How many 60 watt lightbulbs are equivalent to one...Ch. 1 - Convert the temperature of 70°F to °C.Ch. 1 - Convert 30°C to °F.
Ch. 1 - A particular motor rotates at 3000 revolutions per...Ch. 1 - The displacement of a certain object is described...Ch. 1 - Prob. 1.13PCh. 1 - The displacement in meters of a certain vibrating...Ch. 1 - The distance a spring stretches from its “free...Ch. 1 - The following “small angle” approximation for the...Ch. 1 - Prob. 1.17PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Prob. 1.19PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Obtain a linear approximation of the function fh=h...Ch. 1 - The flow rate f in m3/s of water through a...Ch. 1 - Prob. 1.23PCh. 1 - The population data for a certain country are...Ch. 1 - Prob. 1.25PCh. 1 - Quenching is the process of immersing a hot metal...Ch. 1 - The useful life of a machine bearing depends on...Ch. 1 - 1.28 A certain electric circuit has a resistor and...Ch. 1 - 1.29 Water (of volume 425 ml) in a glass measuring...Ch. 1 - Consider the milk container of Example 1.4.2...Ch. 1 - Consider the milk container of Example 1.4.2...
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