Two light springs of force constant k 1 and k 2 and a block of mass m are in one line AB on a smooth horizontal table such that one end of each spring is fixed to rigid supports and the other end is free as shown in the figure. The distance CD between the free ends of the spring is 60 cm. If the block moves along AB with a velocity 120 cm/s in between the springs, calculate the period of oscillation of the block.
Text Solution
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(2.82 s)
Between C and D block will move with constant speed of 120 cm/s. Therefore, period of oscillation will be (starting from C).
T = t CD + 
+ t DC + 
Here, T 1 = 2 π 
and T 2 = 2 π 
and t CD = t DC = 
= 
= 0.5 s
∴ T = 0.5 + 
+ 0.5 + 
(m = 200 g = 0.2 kg)
T = 2.82 s
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