Find the equation of simple harmonic motion for a spring mass system where the mass is hanging off the ceiling with the help of a spring if the initial displacement is 1 ft above equilibrium with initial upward velocity of 2 ft/s. Assume w=1. Write in form y=Asin(x+b). Solve for A, x, and b.

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Asked Oct 6, 2019
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Find the equation of simple harmonic motion for a spring mass system where the mass is hanging off the ceiling with the help of a spring if the initial displacement is 1 ft above equilibrium with initial upward velocity of 2 ft/s. Assume w=1. Write in form y=Asin(x+b). Solve for A, x, and b.

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Expert Answer

Step 1

Given information:

Initial duflacament= tft
Imliad ielesdy
2 /s
-
as
Now Let
asium
us
jaublrm Poyion
>octmdiel
Pesilion
m
help_outline

Image Transcriptionclose

Initial duflacament= tft Imliad ielesdy 2 /s - as Now Let asium us jaublrm Poyion >octmdiel Pesilion m

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Step 2

Finding the simple harmonic equation:

'm
mass im h uilibrwrs
the
The foros ding
Posbion
The
isjm Brudekis
Ym
HJlak dm actndad Position
fras acding on de
m
1
d2y
i Con wrike a:
dt2
may-ky
help_outline

Image Transcriptionclose

'm mass im h uilibrwrs the The foros ding Posbion The isjm Brudekis Ym HJlak dm actndad Position fras acding on de m 1 d2y i Con wrike a: dt2 may-ky

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Step 3

Solving the different...

sluing the aloue ffountal Suadson
Amusoical fundon
got
a
y4)Gfin(wt C2 Ceskot)
C2
Ci
Cosfort)
9A Sim (oi
help_outline

Image Transcriptionclose

sluing the aloue ffountal Suadson Amusoical fundon got a y4)Gfin(wt C2 Ceskot) C2 Ci Cosfort) 9A Sim (oi

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