Jian Hui asked a question from the Practice Springs WeBWorK set last week. At first I thought there was a mistake in the question, but it turns out I was making a mistake with units in my setup.
Here’s my description of the setup, which answers the first part of the problem.
You still have an initial value problem to solve for the second part of the problem, but now this is almost just like the initial value problems you solved in Chapter 5 when you were solving second-order equations.
One difference is that you need to convert your particular solution to a single cosine function like equation 6.1.10 in the textbook. Follow from the bottom of page 270 to the middle of page 271 to see how to do this.