Using Laplace transform- solved2ydt2-4y - 12tGiven that y - 0 and dy-dt - 9 at t - 0-

283

You visited us 283 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Sound Wave:Displacement Equation

Using Laplace...

Question

Using Laplace transform, solve
$\frac{d^{2} y}{d t^{2}} + 4 y = 12 t$
Given that y = 0 and dy/dt = 9 at t = 0.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D d
$\frac{d^{2} y}{d t^{2}} + 4 y = 12 t$
By taking Laplace transform of LHS and RHS and using the property of derivatives of transform $L [f^{n} (t)] = s^{n} F (S) - s^{n - 1} f (0) - s^{n - 2} f^{'} (0) . . . . . . f^{n - 1} (0)$ we get subsidiary equation as :
$(s^{2} + 4) Y - s y (0) - y^{'} (0 = \frac{12}{s^{2}}$
$(s^{2} + 4) Y = \frac{12}{s^{2}} + 5 (0) + 9$
$Y = \frac{12}{s^{2} (s^{2} + 4)} + \frac{9}{s^{2} + 4}$
$Y = \frac{3}{s^{2}} + \frac{3}{s^{2} + 4} + \frac{9}{s^{2} + 4}$
$Y = \frac{3}{s^{2}} + \frac{6}{s^{2} + 4}$
$y (t) = L^{- 1} (Y)$
$y (t) = L^{- 1} (\frac{3}{s^{2}}) + L^{- 1} (\frac{6}{s^{2} + 2^{2}})$
$y (t) = 3 t + 3 sin 2 t$

Suggest Corrections

Similar questions

Q. If

\frac{d^{2} y}{d t^{2}} + y = 0

under the conditions

y = 1, \frac{d y}{d t} = 0

, when t=0 then y is equal to

The function f(t) satisfies the differential equation $\frac{d^{2} f}{d t^{2}} + f = 0$ and the auxiliary conditions, $f (0) = 0, \frac{d f}{d t} (0) = 4$ . The Laplace transform of f(t) is given by

Q. Consider the differential equation

\frac{d^{2} y (t)}{d t^{2}} + 2 \frac{d y (t)}{d t} + y (t) = δ (t) w i t h y (t) |_{t = 0} = - 2 a n d \frac{d y}{d t} |_{t = 0} = 0.

. The numerical value of

\frac{d y}{d t} |_{t = 0}

Q. The Laplace transform of the function

f (t) = k, 0 < t < c = 0, c < t < \infty

, is

Q. The Laplace transform of the function

f (t) = e^{a t} w h e n t > 0

and where

a

is constant is

Join BYJU'S Learning Program

Using Laplace transform, solve d2ydt2+4y=12t Given that y = 0 and dy/dt = 9 at t = 0.

Using Laplace transform, solve
$\frac{d^{2} y}{d t^{2}} + 4 y = 12 t$
Given that y = 0 and dy/dt = 9 at t = 0.