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In case of a simple harmonic motion, if the velocity is plotted along the X-axis and the displacement (from the equilibrium position) is plotted along the Y-axis, the resultant curve happens to be an ellipse with the ratio =("major axis along X")/("minor axis along Y") = 20 pi What is the frequency of the simple harmonic motion? |
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Answer» 100 Hz  `V^(2)/(OQ)^(2) + X^(2)/(OP)^(2) =1`…………..(i) Now, `OQ = AOMEGA[therefore v = ROMEGA = aomega]` and OP =a, where `omega` = angular velocity From eqn. (i) `v^(2)/(a^(2)omega^(2)) + x^(2)/a^(2) =1` Thus, major AXIS, `=2 xx aomega = 2aomega`, minor axis = 2a Given, that `("major axis along X")/("minor axis along Y") = 20pi, therefore (2aomega)/(2a) = 20pi` `f= 10Hz` |
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