Two springs of force constant $$3000$$ $$N/m$$ and $$6000$$ $$N/m$$ are stretched by same force. The ratio of their respective potential energies is

Question

Two springs of force constant $$3000$$ $$N/m$$ and $$6000$$ $$N/m$$ are stretched by same force. The ratio of their respective potential energies  is

Infinity Learn · Accepted Answer

Potential Energy $$PE$$ of simple harmonic oscillator is $$PE$$$$=12kx2$$, $$K=Force$$ constant, $$x=displacement$$ we know that restoring force of a spring is $$F=-$$$$kx$$, here k is force constant, x is displacement ⇒ $$x=-F/k$$, Substitute this in $$PE$$, $$PE$$$$=12k-Fk2$$ ⇒$$PE$$$$=12kF2k2$$ ⇒$$PE$$$$=12F2k$$ ⇒$$PE$$α$$1k$$, by question Force is same, hence taken constant, substitute force constant $$k1$$,$$k2$$ values ⇒$$PE1PE2=k2k1=60003000=21$$

Two springs of force constant 3000 N/m and 6000 N/m are stretched by same force. The ratio of their respective potential energies is

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