An object attached to a spring undergoes simple harmonic motion modeled by the differential equation m + kx 0 where x(t) is the displacement of the mass (relative to equilibrium) at dt2 time t, m is the mass of the object, andk is the spring constant. A mass of 14 kilograms stretches the spring 0.9 meters. Use this information to find the spring constant. (Useg 9.8 meters/second2) k The previous mass is detached from the spring and a mass of 4 kilograms is attached. This mass is displaced 0.3 meters above equilibrium and then launched with an initial velocity of- 0.5 meters/second. Write the equation of motion in the form x(t) leave unknown constants in your equation. = c1 cos(wt) + c2 sin(wt). Do not a(t) : Rewrite the equation of motion in the form x(t) = A sin(wt + ø), where 0 <ø < 2n. Do not leave unknown constants in your equation. a(t)
An object attached to a spring undergoes simple harmonic motion modeled by the differential equation m + kx 0 where x(t) is the displacement of the mass (relative to equilibrium) at dt2 time t, m is the mass of the object, andk is the spring constant. A mass of 14 kilograms stretches the spring 0.9 meters. Use this information to find the spring constant. (Useg 9.8 meters/second2) k The previous mass is detached from the spring and a mass of 4 kilograms is attached. This mass is displaced 0.3 meters above equilibrium and then launched with an initial velocity of- 0.5 meters/second. Write the equation of motion in the form x(t) leave unknown constants in your equation. = c1 cos(wt) + c2 sin(wt). Do not a(t) : Rewrite the equation of motion in the form x(t) = A sin(wt + ø), where 0 <ø < 2n. Do not leave unknown constants in your equation. a(t)
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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An object attached to a spring undergoes simple harmonic motion modeled by the differential
d²x
equation m
+ kx = 0 where x(t) is the displacement of the mass (relative to equilibrium) at
2
dt?
time t, m is the mass of the object, and k is the spring constant. A mass of 14 kilograms stretches
the spring 0.9 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 4 kilograms is attached. This mass is
displaced 0.3 meters above equilibrium and then launched with an initial velocity of -0.5
meters/second. Write the equation of motion in the form x(t)
leave unknown constants in your equation.
= cq cos(wt) + c2 sin(wt). Do not
COS
x(t)
Rewrite the equation of motion in the form x(t) = A sin(wt + ø), where 0 <ø < 2n. Do not
leave unknown constants in your equation.
x(t) :
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