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Question
If x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to ______.
Options
x
– x
16x
– 16x
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Solution
If x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to – 16x.
Explanation:
x = A cos 4t + B sin 4t
`dx/dt` = – A 4 sin 4t + 4B cos 4t
`(d^2x)/(dt^2)` = – 16A cos 4t – 16B sin 4t
= – 16[A cos 4t + B sin 4t]
= – 16x.
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