A \"bob\" or \"simple\" pendulum is a pendulum consisting of a single “point” ma

Question

A "bob" or "simple" pendulum is a pendulum consisting of a single “point” mass attached to a pivot through a connector of negligible weight. A "physical" pendulum has extended size and is a generalization of the bob pendulum. In this experiment we analyze a simple pendulum. The assembly consists of a very thin rod with adaptors and a cylindrical weight as shown in Figure 1 below. Using Newton’s Second Law and the smallangle approximation one finds that the pendulum amplitude follows a cosine function in time with the period given by to

Angle of Pendulum Pendulum Length (cm) Initial Time Final Time Period 6 18 5.5 9.1 12 18 1.8 5.2 18 18 1.8 5.2 24 18 1.75 5.15 30 18 1.55 5

Explanation / Answer

for L = 18 cm or 0.18 m

and theta = 6 deg

T1 = 2pi sqt(Lcos theta/g) = (2*3.14* sqrt(0.18cos6/9.8))

T1 = 0.848 secs

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for L = 18 cm or 0.18 m

and theta = 12 deg

T2 = 2pi sqt(Lcos theta/g)

T2= (2*3.14* sqrt(0.18cos12/9.8))

T2 = 0.841 secs
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for L = 18 cm or 0.18 m

and theta = 18 deg

T2 = 2pi sqt(Lcos theta/g)

T2= (2*3.14* sqrt(0.18cos18/9.8))

T2 = 0.830 secs
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for L = 18 cm or 0.18 m

and theta = 24 deg

T3 = 2pi sqt(Lcos theta/g)

T3= (2*3.14* sqrt(0.18cos24/9.8))

T3 = 0.813 secs
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for L = 18 cm or 0.18 m

and theta = 30 deg

T4 = 2pi sqt(Lcos theta/g)

T4= (2*3.14* sqrt(0.18cos 30/9.8))

T4 = 0.792 secs
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