Free Undamped Oscillations = klo A massm is attached to a spring (with given spring constant k), where the spring force is FR and lo is the initial stretch of the spring. The equation that governs this system is given by 0. The mass is set in motion for mx" + kx = initial conditions x and vo. For each of the equations below: . Find the position function x(t) in the form of C' cos (wo a). • Find the amplitude, period, and frequency of the resulting motion. • Graph of the solution for at least 2 periods Note that the dimensional units should be consistent for all physical constants. 1. A mass of 3 kg is attached to the end of a spring that is stretched 20 cm by a force of 15 N. It is set in motion with initial position хо = O and initial velocity v₁ = − 10 m/s. 2. A body with mass 250 g is attached to the end of a spring that is stretched 25 cm by a force of 9 N. At time t = 0 the body is pulled 1 m to the right, stretching the spring, and set in motion with an initial velocity of 5 m/s to the left.
Free Undamped Oscillations = klo A massm is attached to a spring (with given spring constant k), where the spring force is FR and lo is the initial stretch of the spring. The equation that governs this system is given by 0. The mass is set in motion for mx" + kx = initial conditions x and vo. For each of the equations below: . Find the position function x(t) in the form of C' cos (wo a). • Find the amplitude, period, and frequency of the resulting motion. • Graph of the solution for at least 2 periods Note that the dimensional units should be consistent for all physical constants. 1. A mass of 3 kg is attached to the end of a spring that is stretched 20 cm by a force of 15 N. It is set in motion with initial position хо = O and initial velocity v₁ = − 10 m/s. 2. A body with mass 250 g is attached to the end of a spring that is stretched 25 cm by a force of 9 N. At time t = 0 the body is pulled 1 m to the right, stretching the spring, and set in motion with an initial velocity of 5 m/s to the left.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Free Undamped Oscillations
=
klo
A massm is attached to a spring (with given spring
constant k), where the spring force is FR
and lo is the initial stretch of the spring. The
equation that governs this system is given by
0. The mass is set in motion for
mx" + kx
=
initial conditions x and vo. For each of the
equations below:
.
Find the position function x(t) in the form of
C' cos (wo
a).
• Find the amplitude, period, and frequency of
the resulting motion.
•
Graph of the solution for at least 2 periods
Note that the dimensional units should be
consistent for all physical constants.
1. A mass of 3 kg is attached to the end of a
spring that is stretched 20 cm by a force of 15
N. It is set in motion with initial position
хо = O and initial velocity v₁ = − 10 m/s.
2. A body with mass 250 g is attached to the end
of a spring that is stretched 25 cm by a force
of 9 N. At time t = 0 the body is pulled 1 m to
the right, stretching the spring, and set in
motion with an initial velocity of 5 m/s to the
left.
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