A) \[2\pi \sqrt{\frac{m}{k}}\]
B) \[2\pi \sqrt{\frac{m}{2k}}\]
C) \[2\pi \sqrt{\frac{m}{3k}}\]
D) \[\pi \sqrt{\frac{m}{k}}\]
Correct Answer: B
Solution :
When the particle of mass m at O is pushed by y in the direction of A, the spring A will be compressed by y while spring B and C will be stretched by \[y=y\cos {{45}^{o}}.\]So, that the total restoring force on the mass m is along OA \[{{F}_{net}}={{F}_{A}}+{{F}_{B}}\cos {{45}^{o}}+{{F}_{C}}\cos {{45}^{o}}\] \[=ky+2ky\cos {{45}^{o}}\] \[=ky+2k(y\,cos{{45}^{o}})cos{{45}^{o}}\]\[=2ky\] Also, \[{{F}_{net}}=ky\Rightarrow \,ky=2ky\Rightarrow k2k\] \[T=2\pi \sqrt{\frac{m}{k}}=2\pi \sqrt{\frac{m}{2k}}\]You need to login to perform this action.
You will be redirected in
3 sec