Question

The mass is numerically equal to 2 times the instantaneous velocity. Assume the mass is driven by an external force equal to f(t) = 12cos (2t) + 3sin (2t). Find the initial conditions.

You can proceed to determine the initial conditions based on the given information and external force function.

Answer 1

The initial conditions can be determined using the given external force function and the equation for the mass. The initial conditions are x(t) = ± √(2E/k) cos [(√k/m) t].

Step-by-step explanation:

The mass in this case is numerically equal to 2 times the instantaneous velocity.

Given that the mass is driven by an external force equal to f(t) = 12cos (2t) + 3sin (2t), we can find the initial conditions. To determine the initial conditions, we can use the equations for the initial kinetic energy and potential energy.

Let's assume the initial potential energy is 2E.

From this, we can solve for x and find that x(t) = ± √(2E/k) cos [(√k/m) t].

Therefore, the initial conditions are given by x(t) = ± √(2E/k) cos [(√k/m) t].