The differential equation obtained on eliminating A and B from y=…

MCQ

The differential equation obtained on eliminating A and B from $\text{y}=\text{A}\cos\omega\text{t}+\text{B}\sin\omega\text{t}$ is:

A
$\text{y}''+\text{y}'=0$
B
$\text{y}''-\omega^{2}\text{y}=0$
✓
$\text{y}''=-\omega^{2}\text{y}=0$
D
$\text{y}''+\text{y}=0$

✓

Answer

Correct option: C.

$\text{y}''=-\omega^{2}\text{y}=0$

We have,
$\text{y}=\text{A}\cos\omega\text{t}+\text{B}\sin\omega\text{t}\ ...(\text{i})$
Differentiating both sides of (i) with respect to x, we get
$\frac{\text{dy}}{\text{dt}}=-\text{A}\omega\sin\omega\text{t}+\text{B}\omega\cos\omega\text{t}\ ...(\text{ii})$
Differentiating both sides of (ii)
$\frac{\text{d}^{2}\text{y}}{\text{dt}^{2}}=-\text{A}\omega^{2}\cos\omega\text{t}+\text{B}\omega^{2}\sin\omega\text{t}$
$\Rightarrow \frac{\text{d}^{2}\text{y}}{\text{dt}^{2}}=-\omega^{2}(\text{A}\cos\omega\text{t}+\text{B}\sin\omega\text{t})$
$\Rightarrow \frac{\text{d}^{2}\text{y}}{\text{dt}^{2}}=-\omega^{2}\text{y}$
$\text{y}''=-\omega^{2}\text{y}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from DIFFERENTIAL EQUATIONS→DIFFERENTIAL EQUATIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let the functions $:(-1,1) \rightarrow R$ and $g:(-1,1) \rightarrow(-1,1)$ be defined by $f(x)=|2 x-1|+|2 x+1|$ and $g(x)=x-[x]$,

where $[x]$ denotes the greatest integer less than or equal to $x$. Let $f \circ:(-1,1) \rightarrow R$ be the composite function defined by $(f \circ g)(x)=f(g(x))$. Suppose $c$ is the number of points in the interval $(-1,1)$ at which $f \circ g$ is NOT continuous, and suppose $d$ is the number of points in the interval $(-1,1)$ at which $f \circ g$ is $NOT$ differentiable. Then the value of $c+d$ is. . . . .

→

If $(\vec{a}+3 \vec{b})$ is perpendicular to $(7 \vec{a}-5 \vec{b})$ and $(\vec{a}-4 \vec{b})$ is perpendicular to $(7 \vec{a}-2 \vec{b})$, then the angle between $\vec{a}$ and $\vec{b}$ (in degrees) is $......$

→

The derivative of the function $\cot^{-1}\Big|(\cos2\text{x})^{\frac{1}{2}}\Big|$ at $\text{x}=\frac{\pi}{6}$ is:

→

Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj} A|=64$. Then $|A|$ is equal to:

→

Which of the following is true?

→

Let $\alpha, \beta, \gamma$ be the real roots of the equation, $x ^{3}+ ax ^{2}+ bx + c =0,( a , b , c \in R$ and $a , b \neq 0)$ If the system of equations (in, $u,v,w$) given by $\alpha u+\beta v+\gamma w=0, \beta u+\gamma v+\alpha w=0$ $\gamma u +\alpha v +\beta w =0$ has non-trivial solution, then the value of $\frac{a^{2}}{b}$ is

→

If ${\rm{f}}\left( x \right) = \int\limits_{^{{\pi ^2}/16}}^{{x^2}} {\frac{{\sin x\,\cdot\sin \sqrt \theta }}{{1 + {{\cos }^2}\sqrt \theta }}} .d\theta $ then the value of $f ‘$$\left( {\frac{\pi }{2}} \right)$ , is