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Answer:
The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
Step-by-step explanation:
To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.
First, we will determine y''.
From y = sin(kt)
y' =
y' =
y' = kcos(kt)
Now for y''
y'' =
y'' =
y'' =
Hence, the equation y'' + 144y = becomes
+
∴
±
±
∴ or
Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
The general equation of the sine function y=f(x) is defined as
where A is the Amplitude
B represents the frequency of the function with period equals
C represents the Horizontal shift, For Phase shift= -C/B
D represents the Vertical shift.
The data given that the amplitude of the function A=6
Vertical shift
Horizontal Shift
Now plug in in the general equation of sine function, we get