Which equation describes the magnitude of force needed to deform a spring (F), the distance of deformation (x), and the spring constant (k)? a F = k/x b F = -k/x c F = k + x d F = -kx

d) F = -kx is the right answer. Note that the larger is the deformation, the larger will be the magnitude of the force.

The answers a) and b) don't make sense because for small values of x the magnitude of F will be very large. The answer c) does not make sense because the quantities F and x are measured by different units (N and m, respectively).

PS. Strictly speaking, F = -kx is not the magnitude for positive x because the magnitude must be not negative. In fact, is gives the magnitude and the direction of the force, the latter being opposite to the deformation.