For What Nonzero Values Of $k$ Does the Function $y = A \sin k t + B \cos k t$

question 41

Essay

For what nonzero values of $k$ does the function $y = A \sin k t + B \cos k t$ satisfy the differential equation $y ^ { tt } + 100 y = 0$ for all values of $A$ and $B$ ?
a. $k = 10$
b. $k = - 100$
c. $k = - 10$
d. $k = 100$
e. $k = 1$

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Definitions:

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The state of the atmosphere at a specific time and place, including factors such as temperature, humidity, and wind velocity.

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