Shown in the figure are four different pendulums. Find the period of each pendul

Question

Shown in the figure are four different pendulums.

Find the period of each pendulum when it is pulled 20? to the right and then released.

(a) 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 =

(b) 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 =

(c) 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 =

(d) a mass M is attached to a massless string of length 1 2 L (Use any variable or symbol stated above along with the following as necessary: g.)

T =

Shown in the figure are four different pendulums. Find the period of each pendulum when it is pulled 20? to the right and then released. (a) 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 = (b) 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 = (c) 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 = (d) a mass M is attached to a massless string of length 1 2 L (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

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