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a small block oscillates back and forth on a smooth concave surface of radius R . find the time prriod of small oscillation

a small block oscillates back and forth on a smooth concave surface of radius R . find the time prriod of small oscillation


 

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1 Answers

vikas askiitian expert
509 Points
11 years ago

applying conservation of energy

mv2/2  = mgR(1-sin@)                 (@ is inclination with verticle )

differentiating this eq wrt time

mvdv/dt = mgRsin@d@/dt

  dv/dt = a ,  d@/dt = W

mva = mgRsin@W

for small angle sin@ is equal to @

mva = mgR@W

 now v = wR , & a = alfa(R)

alfa(algular acc) = g@/R

alfa = W2@  so

  W = (g/R)1/2

T = 2pi/W = 2pi(R/g)1/2

 

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