Question

For a spring-mass system (with no damper) initially at rest ((0) = x'(0) = 0), which satisfies the differential equation +=2sin(t), what is the solution for (t)?

Answer 1

The solution for the spring-mass system with the given differential equation is x(t) = ± √(2E/k) cos [(√k/m) t].

Step-by-step explanation:

The solution for the spring-mass system with the given differential equation is:

x(t) = ± √(2E/k) cos [(√k/m) t]

Where:

• x(t) represents the displacement of the mass from its equilibrium position at time t
• E is the total mechanical energy of the system
• k is the spring constant
• m is the mass of the system

The solution can be obtained by applying the initial conditions and solving for x(t).