Suppose a 0.3-kg mass on a spring that has been compressed 0.10 m has elastic potential energy of 1.0 j. how much further must the spring be compressed to triple the elastic potential energy?

Not sure what that mass was supposed to do there

if the spring was compressed 0.1m and has E=1.0 J

than

E=F*d/2=k*d*d/2 wich means

k=2*E/d^2 = 2 * 1J / 0.01m^2 = 200 N/m

so

for E=3J we have E=k*d^2/2 = >

d = sqrt (2*E/k) = sqrt (2*3J/200 N/m) = sqrt (0.03) m = 0.17 m

this means that the spring has to be compressed an aditional 0.07 m to triple the energy

(still not sure what that 0.3 kg mass has to do with it)