| A mass m is connected to four ideal springs of same force constant k as shown below. |
 |
| This system is placed on a horizontal frictionless surface. Time period of oscillation when mass is slightly displaced is |
A) \[2\pi \sqrt{\frac{m}{k}}\]
B) \[2\pi \sqrt{\frac{m}{3k}}\]
C) \[2\pi \sqrt{\frac{3m}{4k}}\]
D) \[2\pi \sqrt{\frac{2m}{5k}}\]
Correct Answer: B
Solution :
| For displacement x, |
| Force on mass m is |
| \[{{F}_{net}}=ma=-(kx+kx+2k\left( \frac{x}{2} \right)\] |
| \[\Rightarrow \,\,a=-\frac{3k}{m}.x\] |
| So, \[T=2\pi \sqrt{\frac{m}{3k}}\] |
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