Question

in which k is a positive constant. the particle passes through the origin with speed v0 at time t = 0. findx as a function of t

Answer 1

x(t) can be expressed as a function of time using the initial conditions and constants given, where x(t) = ±√(2E/k) cos[(√k/m) t], describing the particle's position over time.

Step-by-step explanation:

The question involves finding the position as a function of time for a particle moving along the x-axis, where we have initial conditions and a constant k influencing the motion. Given that the particle passes through the origin at t = 0 with speed v0, we can determine the function describing its position over time. The initial kinetic energy at t = 0 is zero and the initial potential energy is given by 1/2 k x0² = E, from which we derive that x0 = ±√(2E/k). Using trigonometric identities, we convert sine to cosine to obtain x(t) = ±√(2E/k) cos[(√k/m) t].