doubling which quantity would cause the largest increase in a springs elastic potential energy?\no…

Explanation:

Step1: Recall elastic - potential - energy formula

The elastic potential energy of a spring is given by $U = \frac{1}{2}kx^{2}$, where $k$ is the spring constant and $x$ is the displacement from the equilibrium position. Mass and gravitational acceleration are not part of this formula for elastic potential energy of a spring.

Step2: Analyze effect of doubling each relevant quantity

If we double the spring constant $k$ (new $k'=2k$), the new potential energy $U'=\frac{1}{2}(2k)x^{2}=2\times\frac{1}{2}kx^{2}=2U$. If we double the displacement $x$ (new $x' = 2x$), the new potential energy $U'=\frac{1}{2}k(2x)^{2}=\frac{1}{2}k\times4x^{2}=4U$.

Answer:

displacement