A particle of mass m is restricted to move without friction on the x-axis. This particle is connected to a fixed point P a distance d from the x axis by a spring with constant k and length at rest l_0. Working in the two-dimensional plane (x, y), we will denote the coordinates of the particle by (x, 0) while the point P has coordinates (0, d). Find the equilibrium positions of the particle and discuss their stability. In the case where the equilibrium positions are stable, find the period of the small oscillations near equilibrium. Hint: You will want to distinguish the cases d > l_0 , and d < l_0 (ignore the special case d = l_0).

i think the answer is a, hope this is right, that would be my best guess.

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.

well clustered together.

points close on a scatter diagram

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle