
244 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
PROBLEMS
1. Find the linear harmonic oscillator approximation for the potential energy given by
V(x) = ax
−2
+ bx
2
, a,b > 0.
2. A hydrometer oats in a liquid of density d. It is slightly depressed from its normal position
of equilibrium and periodic motion about the equilibrium results. Show that the period of
oscillations is given by
τπ= 2
W
gAd
where g is the local gravitational acceleration, W is the weight of the hydrometer, and A is
the cross-sectional area (Figure 7.30).
3. A straight, uniform stick having a length 2b (meter) and a mass M (kg) is freely pivoted at
one end. Find ...