The following problems consider the “beats” that occur when the forcing term of a differential equation causes “slow" and “fast” amplitudes. Consider the general differential equation a y ″ + b y = cos ( ω t ) that governs undamped motion. Assume that b a ≠ ω . 138. Find the general solution to this equation ( Hint: call ω 0 = b / a ).
The following problems consider the “beats” that occur when the forcing term of a differential equation causes “slow" and “fast” amplitudes. Consider the general differential equation a y ″ + b y = cos ( ω t ) that governs undamped motion. Assume that b a ≠ ω . 138. Find the general solution to this equation ( Hint: call ω 0 = b / a ).
The following problems consider the “beats” that occur when the forcing term of a differential equation causes “slow" and “fast” amplitudes. Consider the general differential equation
a
y
″
+
b
y
=
cos
(
ω
t
)
that governs undamped motion. Assume that
b
a
≠
ω
.
138. Find the general solution to this equation (Hint: call
ω
0
=
b
/
a
).
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