Word Count : 289

---

To solve the given initial value problem using Laplace transforms, we follow these steps: ### Step 1: Take the Laplace Transform of the Equation The given equation is: \[ \frac{d^2y}{dt^2} + \omega^2 y = \cos(\omega t) \] Taking the Laplace Transform on both sides: \[ \mathcal{L} \left[ \frac{d^2y}{dt^2} _______ ____ ________ _________ ______ ________ ________.
__________ ________ _________ ____ _________ _____ ______ __________.
______ __________ _________ ___ ____ ______.
___ ________ __________ ____ _________ _____ _______ __________ ______ _________.
_____ __________ ________ ____ __________.
____ ____ ____ ______ ____.
_____ ____ _________ _________ __________ ____.
_____ _________ __________ ____ __________ __________ ______ __________ ______ __________ _________ ____.
________ ___ _______ _______ __________ ______.
_____ _________ _______ ________ ____ _____ ______ __________ ________.
_______ ______ __________ ___ ______.
____ _____ ________ _________ __________ _____ ___ __________ ______ ___ _________ _________.
____ ________ _____ ____ ______ ___.
_________ ______ _____ ___ _______ _______ __________ ________ _______ _________ _________ ____.
____ ________ _____ _____ ________ ______ _________ _______ ____ __________ ________.
________ ___ ___ _________ ___ __________ ______ _____.
_____ ___ __________ _____ _______ ______.
____ _________ ______ __________ ___ _________ _________ ___ ______ _______ ________.
_______ _____ _________ _________ ________ ________ __________ _________ ______ ________ _______ __________.
________ ____ __________ ___ _______ _________ ____ ___ _____ ___ __________ _______.
____ ___ ____ ___ __________ ________ ______ _________ ___ _____.
_________ ______ ______ _______ ___ ____ _______ _________ ___ _____ _______ ________.
________ __________ ____ _______ __________.
___ ___ _________ ___ __________ __________ ____ ___ _________ ________.
_________ ______ ________ __________ ___.
______ _________ ___ ________ _______.
___ ___ _________ ___ ____ ________ _________.
_______ ____ ___ __________ ____ ________.
___ ________ _______ ____ _________ __________ __________ _____ ________ ________.
_________ ____.
Get Full Answer on WhatsApp