A spring executes S.H.M. with mass $10 \mathrm{~kg}$ attached to it. The force constant of the spring is $10…

A spring executes S.H.M. with mass $10 \mathrm{~kg}$ attached to it. The force constant of the spring is $10 \mathrm{~N} / \mathrm{m}$. If at any instant its velocity is $40 \mathrm{~cm} / \mathrm{s}$, the displacement at that instant is (Amplitude of S.H.M. $=0.5 \mathrm{~m}$ )
  1. $0.3 \mathrm{~m}$
  2. $0.2 \mathrm{~m}$
  3. $0.4 \mathrm{~m}$
  4. $0.45 \mathrm{~m}$

Solution

$\begin{array}{l} V=0 \sqrt{A^{2}-x^{2}}=\sqrt{\frac{k}{m}} \cdot \sqrt{A^{2}-x^{2}} \\ k=10 \mathrm{~N} / \mathrm{m}, \mathrm{m}=10 \mathrm{~kg}, A=0.5 \mathrm{~m} \\ V=40 \mathrm{~cm} / \mathrm{s}=0.4 \mathrm{~m} / \mathrm{s} \end{array}$ Substituting the values and solving we get $\mathrm{x}=0.3 \mathrm{~m}$ .

Asked in: MHT CET 2020 (14 Oct Shift 2)

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