The frequency of the mass when it is displaced slightly is

1.	The frequency of the mass when it is displaced slightly is
Answer» `upsilon=(1)/(2pi)sqrt((k_(1)k_(2))/((k_(1)+k_(2))m))` `upsilon=(1)/(2pi)sqrt((k_(1)+k_(2))/(m))` `upsilon=(1)/(2pi)sqrt((k_(1)k_(2))/(m))` `upsilon=(1)/(2pi)sqrt((k_(1)+k_(2))/(k_(1)k_(2)m))` Solution :Suppose the mass m is DISPLACED slightly towards right. Then the spring on LEFT will be EXTENDED and the spring on right will be compressed. The equation of MOTION for the mass is given by `m(d^(2)x)/(dt^(2))=-k_(1)x-k_(2)x=-(k_(1)+k_(2))xor(d^(2)x)/(dt^(2))=-((k_(1)+k_(2))/(m))x=-omega^(2)x` where `omega^(2)=(k_(1)+k_(2))/(m)oromega=sqrt((k_(1)+k_(2))/(m))` `therefore` Frequency, `upsilon=(omega)/(2pi)=(1)/(2pi)sqrt((k_(1)+k_(2))/(m))`

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