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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
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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