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Question

Two springs are connected to a block of mass $$M$$ placed on a frictionless surface as shown below. If both the springs have a spring constant $$k$$, the frequency of oscillation of block is
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A
12πkM
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B
12πk2M
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C
12π2kM
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D
12πMk
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Solution

The correct option is B $$\displaystyle \frac {1}{2\pi}\sqrt{\frac {k}{2M}}$$
For spring block system, $$\displaystyle n=\frac {1}{2\pi}\sqrt{\frac {k}{M}}$$
Here two springs are joined in series so, total spring constant, $$\displaystyle k_R=\frac {k_1k_2}{k_1+k_2}$$
$$\displaystyle k_R=\frac {k.k}{2k}=\frac {k}{2}$$
So, $$\displaystyle n=\frac {1}{2\pi}\sqrt{\frac {k}{2M}}$$

Physics

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