A spring with constant k = 7 N/m hanging from the ceiling is placed at its lower end with an object of 1 N, which makes it remain in equilibrium. The weight is then pulled 0.7 m above the equilibrium position and released with no initial velocity. There is no damping force acting on the system. If x(t) represents the displacement of the weight, in meters, from the equilibrium point and taking upwards as the positive direction, an equation that describes the position of the weight as a function of time t (in seconds) is: If necessary, use the gravity constant g as g=9.8 m/s?. a) ¤(t) = 0.35 (etv68.6 + e=tv68.6 ot/68.6 -t/68.6 b) x(t) = 0.35 sen(t/68.6) c) æ(t) = 0.7 cos(t/68.6) 0) #(t) = 0.7 (etv®%o +etv888) et/68.6
A spring with constant k = 7 N/m hanging from the ceiling is placed at its lower end with an object of 1 N, which makes it remain in equilibrium. The weight is then pulled 0.7 m above the equilibrium position and released with no initial velocity. There is no damping force acting on the system. If x(t) represents the displacement of the weight, in meters, from the equilibrium point and taking upwards as the positive direction, an equation that describes the position of the weight as a function of time t (in seconds) is: If necessary, use the gravity constant g as g=9.8 m/s?. a) ¤(t) = 0.35 (etv68.6 + e=tv68.6 ot/68.6 -t/68.6 b) x(t) = 0.35 sen(t/68.6) c) æ(t) = 0.7 cos(t/68.6) 0) #(t) = 0.7 (etv®%o +etv888) et/68.6
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:A spring with constant k = 7 N/m hanging from the ceiling is placed at its lower end with an object
of 1 N, which makes it remain in equilibrium. The weight is then pulled 0.7 m above the
equilibrium position and released with no initial velocity. There is no damping force acting on the
system. If x(t) represents the displacement of the weight, in meters, from the equilibrium point
and taking upwards as the positive direction, an equation that describes the position of the weight
as a function of time t (in seconds) is:
If necessary, use the gravity constant g as g=9.8 m/s?.
etv68
a) x(t) = 0.35 (
68.6
+e-tv68.6
b) x(t) = 0.35 sen(t/68.6)
c) x(t) = 0.7 cos(t/68.6)
d) æ(t) =
0.7 (etv68.6
tetv68.6
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