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Question

Consider a spring that exerts restoring force F=−kx for x>0,F=−2kx for x<0. A mass m on a frictionless surface is attached to this spring, displaced to x=A and released. Find the time period of motion.

A
5.36mk
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B
5.36m2k
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C
5.362mk
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D
None
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Solution

The correct option is A 5.36√mkGiven, F=−kx,x>0 and F=−2kx,x<0 For half time-period, Fnet=−kx ∴a=(−km)x As T=2πω, hence t1=2π2√k/m=π√k/m Again, for other half time-period, Fnet=−2kx ∴a=(−2km)x As T=2πω, hence t2=2π2√2k/m=π√2k/m Hence, the total time period is T=t1+t2=π√k/m+π√2k/m=5.36√m/k

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