An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x m +kx = dt² :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 12 kilograms stretches the spring 0.2 meters. Use this information to find the spring constant. (Use g = 9.8 meters/second²) k = The previous mass is detached from the spring and a mass of 10 kilograms is attached. This mass is displaced 0.95 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) = Submit Question
An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x m +kx = dt² :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 12 kilograms stretches the spring 0.2 meters. Use this information to find the spring constant. (Use g = 9.8 meters/second²) k = The previous mass is detached from the spring and a mass of 10 kilograms is attached. This mass is displaced 0.95 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) = Submit Question
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:An object attached to a spring undergoes simple harmonic motion modeled by the differential equation
d²x
m
+kx
=
dt²
: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 12 kilograms stretches the spring 0.2 meters.
Use this information to find the spring constant. (Use g = 9.8 meters/second²)
k =
The previous mass is detached from the spring and a mass of 10 kilograms is attached. This mass is
displaced 0.95 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) =
Submit Question
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