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प्रश्न
A body of mass 0.8 kg performs linear S.H.M. It experiences a restoring force of 0.4 N when its displacement from the mean position is 4 cm. Determine the force constant and period of S.H.M.
संख्यात्मक
उत्तर
Given:
Mass of the body (m) = 0.8 kg
Restoring force (F) = 0.4 N
Displacement from mean position (x) = 4 cm = 4 × 10−2 m
Calculations:
1. Calculate Force Constant (k):
Using Hooke’s Law,
F = −kx
`k = F/x`
`k = 0.4/(4 xx 10^-2)`
k = 10 N/m
2. Calculate Period of S.H.M. (T):
`T = 2 pi sqrt(m/k)`
`T = 2 pi sqrt(0.8/10)`
T = 2π × 0.2828
T = 1.78 s
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