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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 5.36mk
Given,
F=kx,x>0
and F=2kx,x<0

For half time-period,
Fnet=kx a=(km)x
As T=2πω, hence t1=2π2k/m=πk/m

Again, for other half time-period,
Fnet=2kx a=(2km)x
As T=2πω, hence t2=2π22k/m=π2k/m

Hence, the total time period is
T=t1+t2=πk/m+π2k/m=5.36m/k

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