Question
Shown in the figure are four different pendulums. Find the period of each pendulum when it is pulled 20 degree to the right and then released. a rod has a mass M and a length L (Use any variable or symbol stated above along with the following as necessary: g.) T = a rod has a mass 2M and a length L (Use any variable or symbol stated above along with the following as necessary: g.) T = a mass M is attached to a massless string of a length L (Use any variable or symbol stated above along with the following as necessary: g.) T = a mass M is attached to a massless string of length 1/2L (Use any variable or symbol stated above along with the following as necessary: g.) T =
Explanation / Answer
the rod with uniform massdistribution rotates around point O much like a classical pendulum with effective length equal to 2L/3. a) T=2pi(Leffective/g)^1/2 T=2pi(2L/3g)^1/2 b)time period independent of mass T=2pi(2L/3g)^1/2 c) Leffective = L . T=2pi(L/g)^1/2 d) time period independent of mass T=2pi(L/g)^1/2