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 between E , m , n and a .

Question

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 between E , m , n and a . (JEE 1981)

TestHub · Accepted Answer

[ E ] = k ([ m ] ) x ([ n ] ) y ([ a ] ) z gives [ M L 2 T − 2 ] = k ([ M ] ) x ( [ T − 1 ] ) y ([ L ] ) z . Solving, x = 1 , y = 2 and z = 2 , so E = km n 2 a 2 .

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