with extension x 0 at equilibrium. At time t = 0 the mass is already moving: we have positive constants Xo > 0 and vo> 0. At some timet= to > 0, a short-lived impulse J is applied to the mass. Recognizing that mu = k, the motion of the mass thus satisfies J -6 (t - to) +w2 (6) dt2 m 2.1. Use the Laplace Transform approach to show that the position function of the mass at time t > to is given by the expression sin [w (t - to)] + A sin [wt+ ; r(t) = mw (t > to) (7) (with A > 0), and produce expressions for A, in terms of the initial conditions and other quantities given in the question. 1: C aroccion (7 t1a aaasib wootion of tho

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Chapter2: Second-order Linear Odes
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practice problem 2.1:  need help with what my A and phase angle would be for expression 7

with extension x 0 at equilibrium. At time t = 0 the mass is already moving: we have positive constants
Xo > 0 and vo> 0. At some timet= to > 0, a short-lived impulse J is applied to the mass. Recognizing
that mu = k, the motion of the mass thus satisfies
J
-6 (t - to)
+w2
(6)
dt2
m
2.1. Use the Laplace Transform approach to show that the position function of the mass at time t > to is
given by the expression
sin [w (t - to)] + A sin [wt+ ;
r(t) =
mw
(t > to)
(7)
(with A > 0), and produce expressions for A, in terms of the initial conditions and other quantities
given in the question.
1: C
aroccion (7 t1a
aaasib
wootion of tho
Transcribed Image Text:with extension x 0 at equilibrium. At time t = 0 the mass is already moving: we have positive constants Xo > 0 and vo> 0. At some timet= to > 0, a short-lived impulse J is applied to the mass. Recognizing that mu = k, the motion of the mass thus satisfies J -6 (t - to) +w2 (6) dt2 m 2.1. Use the Laplace Transform approach to show that the position function of the mass at time t > to is given by the expression sin [w (t - to)] + A sin [wt+ ; r(t) = mw (t > to) (7) (with A > 0), and produce expressions for A, in terms of the initial conditions and other quantities given in the question. 1: C aroccion (7 t1a aaasib wootion of tho
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