Final answer:
To solve the initial value problem, initial conditions are used to find the constants in a function x(t). The solution involves relating potential energy to position and a cosine function.
Step-by-step explanation:
The student is asking to solve an initial value problem involving a function x(t) where x(0) is given and helps determine the constants in the general solution of the differential equation. To solve the initial value problem, we use the initial conditions provided to determine the constants in the equation. Once known, we can define the function entirely and solve for x(t). For example, if the energy at the beginning is all potential energy (E), we can relate it to the initial position x0 and spring constant k. Utilizing trigonometric identities and known relationships between potential and kinetic energy, the solution for x(t) involves a cosine function with parameters derived from the energy, spring constant, mass, and initial conditions.