1. The problem statement, all variables and given/known data An object with mass m start its journey on x-axis at point (-l,0) with velocity v. The object feels force which depends on the object's distance to origin. After T second it reaches the origin. What is T? 2. Relevant equations x(t=0)=-l v(t=0)=v f(x)=-kx x(t=T)=0 T=? 3. The attempt at a solution 1: dx/dt = v(t) 2: dt = dx/v(t) [from 1] 3: dv/dt = a(t) = (-k/m) * x(t) 4: dt = m * dv/(-k * x(t)) [from 3] 5: v(t) * dv = (-k/m) * x(t) * dx [put 2 to 3] 6: integrating both sides of 5 and putting the values x=0 and the velocity at the origin (which can be calculated by the energy change with integrating f(x) dx from -l to zero) gives the relation between x and v. 7: Putting x in terms of v (found in 6) to 4 and integrating right side from initial velocity to velocity at the origin gives a time (dt at the left side). But i am not sure about the answer. Any ideas will be great. Thank you.