Abody of mass m is suspended from two light springs of force constant k_(1) and k_(2)(k_(1)) separately. The periods of vertical oscillations are T_(1) and T_(2) respectively. Now the same body is suspended from the same two springs which are first connected in series and then in parallel. The period of vertical oscillations are T_(s) and T_(p) respectively, then

Abody of mass m is suspended from two light springs of force constant

1.	Abody of mass m is suspended from two light springs of force constant k_(1) and k_(2)(k_(1)) separately. The periods of vertical oscillations are T_(1) and T_(2) respectively. Now the same body is suspended from the same two springs which are first connected in series and then in parallel. The period of vertical oscillations are T_(s) and T_(p) respectively, then
Answer» `T_(p)ltT_(1)ltT_(2)ltT_(s)` `T_(s)^(2)=T_(1)^(2)+T_(2)^(2)` `sqrt(T_(s))=sqrt(T_(1))+sqrt(T_(2))` `(1)/(T_(p)^(2))=(1)/(T_(1)^(2))+(1)/(T_(2)^(2))` SOLUTION :`T_(1)=2pisqrt((m)/(k_(1))), T_(2)=2pisqrt((m)/(k_(2)))` `T_(s)=2pisqrt((m)/((k_(1)k_(2))//(k_(1)=k_(2))))` `T_(p)=2pisqrt((m)/((k_(1)+k_(2))))` From above we note that `T_(s)gtT_(2)gtt_(1)gtT_(p),i.e.,` OPTION (a) is CORRECT. `(1)/(T_(p)^(2))=(k_(1)+k_(2))/(4pi^(2)m)=(k_(1))/(4pi^(2)m)+(k_(2))/(4pi^(2)m)` `=(1)/(T_(1)^(2))+(1)/(T_(2)^(2)),i.e.,` option (d) is correct. `T_(s)^(2)=(4pi^(2)m(k_(1)+k_(2)))/(k_(1)k_(2))=(4pi^(2)m)/(k_(2))+(4pi^(2)m)/(k_(1))` `=T_(2)^(2)+T_(1)^(2), i.e.,` option (b) is correct.