InterviewSolution
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InterviewSolution
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Determine the natural frequency of vibration of the `100N` disk. Assume the disk does not slip on the inclined surface. |
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Answer» In equilibrium, `mg sin theta = kx_(0)`…(i) When displaced by `x`, `E = (1)/(2) mv^(2) + (1)/(2) I omega^(2) + (1)/(2)k(x + x_(0))^(2) - mgx sin theta` Since, E = constant `(dE)/(dt) = 0` `0 = mv((dv)/(dt)) + I omega ((d omega)/(dt)) + k (x + x_(0))(dx)/(dt) - mg sin theta (dx)/(dt)` Substituting, `(dv)/(dt) = a, omega = (v)/(R), I = (1)/(2)mR^(2)` `(d omega)/(dt) = alpha = (a)/(R),(dx)/(dt) = v` and `kx_(0) = mg sin theta` We get, `3ma = - 2kx` `:. f = (1)/(2x)sqrt|(a)/(x)| = (1)/(2pi) sqrt((2k)/(3m))` Substituting the values, `f = (1)/(2pi)sqrt(((2 xx 200)/(3 xx 100))/(9.8))` `= 0.56 Hz`. |
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