For the following problem, set up and solve the differential equations. 141. An opera singer is attempting to shatter a glass by singing a particular note. The vibrations of the glass can be modeled by y ″ + a y = cos ( b t ) , where y ″ + a y = 0 represents the natural frequency of the glass and the singer is forcing the vibrations at cos ( b t ) . For what value b would the singer be able to break that glass? ( Note: in order for the glass to break, the oscillations would need to get higher and higher.)
For the following problem, set up and solve the differential equations. 141. An opera singer is attempting to shatter a glass by singing a particular note. The vibrations of the glass can be modeled by y ″ + a y = cos ( b t ) , where y ″ + a y = 0 represents the natural frequency of the glass and the singer is forcing the vibrations at cos ( b t ) . For what value b would the singer be able to break that glass? ( Note: in order for the glass to break, the oscillations would need to get higher and higher.)
For the following problem, set up and solve the differential equations.
141. An opera singer is attempting to shatter a glass by singing a particular note. The vibrations of the glass can be modeled by
y
″
+
a
y
=
cos
(
b
t
)
, where
y
″
+
a
y
=
0
represents the natural frequency of the glass and the singer is forcing the vibrations at
cos
(
b
t
)
. For what value b would the singer be able to break that glass? (Note: in order for the glass to break, the oscillations would need to get higher and higher.)
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