In the laboratory, a student studies a pendulum by graphing the angle that the s

Question

In the laboratory, a student studies a pendulum by graphing the angle that the string makes with the vertical as a function of time t , obtaining the graph shown in the figure (Figure 1) .

Part A) What is the period of the pendulum's motion?

Express your answer in seconds to one decimal place.

Part B) What is the frequency of the pendulum's motion?

Express your answer in hertz to three significant figures.

Part C) What is the angular frequency of the pendulum's motion?

Express your answer in radians per second to three significant figures.

Part D) What is the amplitude of the pendulum's motion?

Express your answer in degrees to one decimal place.

Part E) How long is the pendulum?

Express your answer in meters to three significant figures.

Part F) Is it possible to determine the mass of the bob?

Explanation / Answer

Part A) What is the period of the pendulum's motion?

From the graph of this motion, the period (T) = 1.6 s

Part B) What is the frequency of the pendulum's motion?

frequency = 1/T = 0.625 Hz

Part C) What is the angular frequency of the pendulum's motion?

angular frequency = 0.625 x 24° = 15° per sec

Part D) What is the amplitude of the pendulum's motion?

Amplitude = 6°

Part E) How long is the pendulum?

T = 2L/g = 1.6
1.6/2 = L/g
0.2546479 = L/g
L/g = 0.064846
L = (9.81)(0.064846) = 0.64 m

Part F) Is it possible to determine the mass of the bob

It is not possible to determine the mass of the bob of any pendulum by observing its motion, this is because the acceleration due to gravity is the same for any object regardless of mass.

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