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Answer the question please

Answer the question please

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Grade:12th pass

1 Answers

Sandeep Pathak
askIITians Faculty 25 Points
10 years ago
Since we are talking about small oscillations, we have to consider them about the equilibrium position. Let’s call upper spring, spring 1 and lower spring, spring 2. Also assume the equilibrium extensions of springs arex_1^0and x_2^0respectively.

Then tension in lower string isT_2 = 3kx_2^0=mg.
Tension in upper string isT_1 = 2T_2=6kx_2^0 = 2kx_1^0\Rightarrow x_1^0 = 3x_2^0.

Now assume that the two springs are extended by x_1 and x_2 respectively.Then the mass lowers by an amountx=2x_1+x_2. Let us calculate restoring force on mass
F=3k(x_2^0+x_2)-mg=3kx_2

Again, useT_1 = 2T_2\Rightarrow x_1 = 3x_2

Thus,
x=2x_1+x_2=7x_2\Rightarrow x_2 = \frac{x}{7}

Restoring force,
F=\frac{3kx}{7}\Rightarrow \omega = \sqrt{\frac{7m}{3k}}\Rightarrow n=3

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