Question

What is the formula for the displacement of an oscillator when starting at x = 0 and an initial velocity?

Answer 1

The displacement of an oscillator starting at x = 0 with an initial velocity can be obtained using the kinematic equation
`x = x_o + v_ot + (1/2)at^2`, assuming xo is zero and integrating velocity over time.

Step-by-step explanation:

The formula for the displacement of an oscillator starting at x = 0 with an initial velocity (
`v_o`) can be derived using the equations of simple harmonic motion. Displacement in simple harmonic motion as a function of time is given by
`x(t) = X cos(\omega t)`, where X is the amplitude and ω is the angular frequency. The initial velocity can affect where the oscillator will be at a given time.

If we know the initial velocity, acceleration (a), and the time (t), we can use the kinematic equation
`x = x_o + v_ot + (1/2)at^2` to find the displacement, assuming xo is zero. To give an exact formula, we would need the specific values for vo, a, and t.