Question

Solve the following initial value problem. StartFraction d squared s Over dt squared EndFraction d2s dt2equals=negative 16 Bold sine (4 t minus StartFraction pi Over 2 EndFraction )−16sin4t− π 2​, s prime (0 )equals 500s′(0)=500​, ​s(0)equals=0

Answer 1

To solve the initial value problem, we need to integrate the given acceleration function twice and use the initial conditions to find the constants of integration.

Step-by-step explanation:

To solve the initial value problem d2s/dt2 = -16sin(4t - π/2) - 16sin4t - π/2, s'(0) = 500, s(0) = 0, we can follow these steps:

Integrate the given acceleration function twice to find the expression for s(t).

Use the initial condition s'(0) = 500 to solve for the constant of integration.

Use the initial condition s(0) = 0 to solve for another constant of integration.

After following these steps, you should obtain the solution to the initial value problem.

Answer 2

Step-by-step explanation:

Given the initial value problem

d²S/dt² = -16sin4t-π/2 if s(0) = 0, s'(0) = 500

We will integrate the given differential equation twice and substitute the initial values into our resulting answer as shown on the attachment.