## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

$(U_s)_d > (U_s)_c > (U_s)_b = (U_s)_a$
When a spring is compressed a distance of $x$, the elastic potential energy stored in the spring is $U_s = \frac{1}{2}kx^2$, where $k$ is the spring constant. We can find the elastic potential energy stored in spring a. $(U_s)_a = \frac{1}{2}kd^2$ We can find the elastic potential energy stored in spring b. $(U_s)_b = \frac{1}{2}kd^2$ We can find the elastic potential energy stored in spring c. $(U_s)_c = \frac{1}{2}(2k)d^2$ $(U_s)_c = kd^2$ We can find the elastic potential energy stored in spring d. $(U_s)_d = \frac{1}{2}k(2d)^2$ $(U_s)_d = 2kd^2$ We can rank elastic potential energy in the springs in order from most to least: $(U_s)_d > (U_s)_c > (U_s)_b = (U_s)_a$