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The energy $E$ of an oscillating body in simple harmonic motion depends on its mass $m$ , frequency $n$ and amplitude $a$ . Using the method of dimensional analysis, find the relation analysis, find the relation between $E, m, n a n d a$ .

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x=-1, y=2, z=2

x=1, y=2, z=2

x=2, y=2, z=2

x=-2, y=2, z=2

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detailed solution

Correct option is B

[E]=k[ m]x[n]y[a]zwhere, k is a dimensionless constant. ∴ ML2 T-2=k[M]x T-1y[ L]zSolving, we getx=1, y=2 and z=2 ∴E=kmn2a2

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The energy E of an oscillating body in simple harmonic motion depends on its mass m, frequency n and amplitude a. Using the method of dimensional analysis, find the relation analysis, find the relation between E, m, n and a.

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Ready to Test Your Skills?

free study material

The energy $E$ of an oscillating body in simple harmonic motion depends on its mass $m$ , frequency $n$ and amplitude $a$ . Using the method of dimensional analysis, find the relation analysis, find the relation between $E, m, n a n d a$ .