Question

Let $y=a\cos t+b\sin t$ then $\frac{d^{2}y}{d{t}^2}=$

• A. $y$
• B. $-y$
• C. $2y$
• D. none of these

Answer 1

Answer: (B)

$-y$

Given,

$y=a\cos t+b\sin t$......(1).

Now differentiating both sides with respect to $t$ we get,

$\frac{dy}{dt}=-a\sin t+b\cos t$

Again differentiating both sides with respect to $t$ we get,

$\frac{d^{2}y}{d{t}^2}=-a\cos t-b\sin t$

or, $\frac{d^{2}y}{d{t}^2}=-y$. [ Using (1)]