When a particle is performing linear SHM its $$KE$$ is two times its $$PE$$ at a position ‘A’ and its $$PE$$ is two times its $$KE$$ at another position ‘B’. Find ratio of KEA to KEB

Question

When a particle is performing linear SHM its $$KE$$ is two times its $$PE$$ at a position ‘A’ and its $$PE$$ is two times its $$KE$$ at another position ‘B’. Find ratio of KEA  to  KEB

Infinity Learn · Accepted Answer

At A,        $$KE$$$$=2PE$$,             ⇒$$PE$$$$=$$$$KE$$$$/2$$,                  $$TE$$$$=$$$$KE$$$$+$$$$PE$$,  substitute,$$TE$$$$=$$$$KE$$$$+KE2$$,               ⇒$$TEA=3KEA2---(1)$$ At B,        $$PE$$$$=2KE$$,                  $$TE$$$$=$$$$KE$$$$+$$$$PE$$,  substitute,$$TE$$$$=$$$$KE$$$$+2KE$$,               ⇒$$TEB=3KEB----(2)$$ according to principle of conservation of energy $$TEA=TEB$$ $$3KEA2=3KEB$$ ⇒$$KEAKEB=21$$

When a particle is performing linear SHM its KE is two times its PE at a position ‘A’ and its PE is two times its KE at another position ‘B’. Find ratio of ${KE}_{A}$ to ${KE}_{B}$

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When a particle is performing linear SHM its KE is two times its PE at a position ‘A’ and its PE is two times its KE at another position ‘B’. Find ratio of KEA to KEB

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When a particle is performing linear SHM its KE is two times its PE at a position ‘A’ and its PE is two times its KE at another position ‘B’. Find ratio of ${KE}_{A}$ to ${KE}_{B}$