doubling which quantity would cause the largest increase in a springs elastic potential energy?\ndisplacement…

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 quantity

If we double the spring - constant $k$, the new potential energy $U_{new1}=\frac{1}{2}(2k)x^{2}=2\times(\frac{1}{2}kx^{2}) = 2U$. If we double the displacement $x$, the new potential energy $U_{new2}=\frac{1}{2}k(2x)^{2}=\frac{1}{2}k\times4x^{2}=4\times(\frac{1}{2}kx^{2}) = 4U$.

Answer:

displacement