A vertical spring stores $0\mathrm{.}962$ J in spring potential energy when a $3\mathrm{.}5-kg$ mass is suspended from it$.($a$)$ By what multiplicative factor does the spring potential energy change if the mass attached to the spring is doubled? $($b$)$ Verify your answer to part $($a$)$ by calculating the spring potential energy when a $7\mathrm{.}0-kg$ mass is attached to the spring.