In the figure shown the spring is relaxed and mass m is attached to the spring. The spring is compressed by 2 A and released at t = 0. Mass m collides with the wall and loses two third of its kinetic energy and returns. Starting from t = 0, find the time taken by it to come back to rest again (instant at which spring is again under maximum compression). Take 
Text Solution
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(17)
The motion starts from position A
the time taken from A to W 2 (t 1 ) = 
Before collision the energy of the system is conserved,
Kinetic energy of the block just before collision
K i = 
K (2A) 2 – 
KA 2 = 
KA 2 & just after collision K f = 
(given) = 
KA 2
Now during motion after collision, the energy is again conserved
Hence, K f + 
KA 2 = 
KA´ 2
A’ = maximum compression after collision ⇒ A´ = A 
ie. Now motion has amplitude A 
Now time taken by block from
W 2 to position B = 
+ 
total time taken = t 1 + t 2 = 
+ 
+ 
+ 
= 
= 
= 17sec 
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