Question
Asked Nov 5, 2019
Forced undamped motion satisfies a differential equation of the form
d2y
by F sin(wt + B)
dt2
a
Find the general solution if
=
wo
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Forced undamped motion satisfies a differential equation of the form d2y by F sin(wt + B) dt2 a Find the general solution if = wo

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check_circleExpert Solution
Step 1

Differential Equation of the undamped forced motion

dy
'y=Fsin (t+ )
dt
This is a non-homogenous diffrential Equation
So
General solution
y C.F. P.1
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dy 'y=Fsin (t+ ) dt This is a non-homogenous diffrential Equation So General solution y C.F. P.1

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Step 2

First calculate the C.F. for the equation. Put L.H.S. is equal to the zero.

dy
dt
or
|y = 0
dt
Put
dt
m2 0
m tio
roots are complex
so. C.F
. Asinot+Bcos oi
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dy dt or |y = 0 dt Put dt m2 0 m tio roots are complex so. C.F . Asinot+Bcos oi

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Step 3

Now, for calculat...

1
F sin (ot B)
f (D)
P.I.=
1
F sin ( t+ B
PI.
By the formula:
1
-sin (a b)
1
sin (ax +b).f(-a)
f(-a2)
0
f(D
1
Fsin ( t+B
P.I.=
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1 F sin (ot B) f (D) P.I.= 1 F sin ( t+ B PI. By the formula: 1 -sin (a b) 1 sin (ax +b).f(-a) f(-a2) 0 f(D 1 Fsin ( t+B P.I.=

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