Three spring mass systems are shown in figure. Assuming gravity free space, find the time period of oscillations in each case. What should be the answer if space is not gravity free?
Text Solution
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2 π 
, k eq. = k 1 + k 2
2 π 
, k eq. = k 1 + k 2
2 π 
, k eq. = 
Answers will remain same
Sol. When spring is stretched by x then restoring force.
F = K 1 x + K 2 x
F = K eq x
K eq x = K 1 x + K 2 x
K eq = K 1 + K 2
T = 2 π 
= 2 π 
When bock is displaced by x from mean position then restoring force.
F = K 1 x + K 2 x
K eq x = K 1 x + K 2 x
K eq = K 1 + K 2
T = 2 π 
= 2 π 
When block is displaced by x and extension in upper spring is x 1 , extension in lower spring is x 2
then F = K 1 x 1
⇒ x 1 = 
F = K 2 x 2
⇒ x 2 = 
F = K eq x
⇒ x = 
x = x 1 + x 2
⇒ 
= 
+ 
⇒ K eq = 
T = 2 π 
= 2 π 
When space is not gravity free then answers do not change as time period of spring mass system is a
independent of gravity.
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