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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $x = A\cos 4t + B\sin 4t$, then ${{{d^2}x} \over {d{t^2}}} = $
  • ✓
    $-16x$
  • B
    $16 x$
  • C
    $x$
  • D
    $-x$
✓

Answer

Correct option: A.
$-16x$
a
(a) $x = A\cos 4t + B\sin 4t$

Differentiate w.r.t. $t,$ 

$\frac{{dx}}{{dt}} = - 4A\sin 4t + 4B\cos 4t$

Again, differentiate w.r.t. $t,$ 

$\frac{{{d^2}x}}{{d{t^2}}} = - 16A\cos 4t - 16B\sin 4t$

$\frac{{{d^2}x}}{{d{t^2}}} = - 16[A\cos 4t + B\sin 4t]$. 

Hence, $\frac{{{d^2}x}}{{d{t^2}}} = - 16x$.

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