A) \[\frac{1}{2\pi }\sqrt{\frac{k}{m}}\]
B) \[\frac{1}{2\pi }\sqrt{\frac{2k}{m}}\]
C) \[\frac{1}{2\pi }\sqrt{\frac{3k}{m}}\]
D) \[\frac{1}{2\pi }\sqrt{\frac{m}{k}}\]
Correct Answer: C
Solution :
Key Idea: The mass executes SHM. When the oscillating mass m is at a distance x towards right from its equilibrium position, then the spring is stretched through distance x while the other spring is compressed through the same distance x. Hence, restoring force exerted by each spring on mass m is in the same direction tending to bring it in its equilibrium position. Let \[{{v}_{e}}=\sqrt{\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}}\] and \[P+\frac{1}{2}\rho {{v}^{2}}+\rho gh=constant\] be the restoring forces produced then \[P+\frac{1}{2}\rho {{v}^{2}}+\rho gh=constant\] and \[\Omega \] total restoring force is \[\Omega \]. Hence, frequency \[\Omega \]
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