An elastic spring is attached to the ceiling. A block with mass m is attached to the spring, and the spring is stretched by the distance *l*.

If two blocks with total mass 2m are attached, the spring is displaced by the distance 2*l*. The forces on the block are the weight mg [downward] and the Elastic Spring Forces [upwards]. Because the block is in mechanical equilibrium, the net force on the block is zero. We conclude that the elastic force is a linear restoring force,

**F _{elast} = – kx,**

where k is the spring constant with unit **[k] = [F]/[x] = N/m.** We thus have F > 0 for x < 0 and F < 0 for x > 0.

We consider a block with mass m sliding on a frictionless horizontal surface. The force along the horizontal direction is given by **F = F _{elast} = -kx** so that the equation of motion of the block follows F = ma = – kx, or

** a = – (k/m)x.**

We know that, ω^{2} = k/m so that

**T= 2π √(m/k)**

Springs are stiffer for greater values of the spring constant. **T= 2π √(m/k),** then shows that stiffer springs oscillate with shorter periods.