A) \[\frac{1}{6}\pi \sqrt{\frac{k}{m}}\]
B) \[\sqrt{\frac{k}{m}}\]
C) \[\frac{2\pi }{3}\sqrt{\frac{k}{m}}\]
D) \[\frac{\pi }{4}\sqrt{\frac{k}{m}}\]
Correct Answer: C
Solution :
[c] The total time from A to C \[{{t}_{AC}}={{t}_{AB}}+t=(T/4)+{{t}_{BC}}\] Where T=time period of oscillation offspring mass system \[{{t}_{BC}}\]can be obtained form, \[BC=A\,B\sin {{(2\pi /T)}^{{{t}_{BC}}}}\] Putting \[\frac{BC}{AB}=\frac{1}{2}\]we obtain \[{{t}_{BC}}=\frac{T}{12}\] \[\Rightarrow {{t}_{AC}}=\frac{T}{4}+\frac{T}{12}=\frac{2\pi }{3}\sqrt{\frac{m}{k}}\].You need to login to perform this action.
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