The angular displacement θ (in radians) for a simple pendulum is given by θ = 0.175 sin π t . a. Determine the period of the pendulum. b. How many swings are completed in 1 sec ? c. To the nearest degree, what is the maximum displacement of the pendulum? d. The length L of a pendulum is related to the period T by the equation T − 2 π L g , where g is the acceleration due to gravity. Find the length of the pendulum to the nearest meter g = 9.8 m / s e c 2 .
The angular displacement θ (in radians) for a simple pendulum is given by θ = 0.175 sin π t . a. Determine the period of the pendulum. b. How many swings are completed in 1 sec ? c. To the nearest degree, what is the maximum displacement of the pendulum? d. The length L of a pendulum is related to the period T by the equation T − 2 π L g , where g is the acceleration due to gravity. Find the length of the pendulum to the nearest meter g = 9.8 m / s e c 2 .
Solution Summary: The author calculates the period of the pendulum and the number of swings completed in 1sec.
The angular displacement
θ
(in radians) for a simple pendulum is given by
θ
=
0.175
sin
π
t
.
a. Determine the period of the pendulum.
b. How many swings are completed in
1
sec
?
c. To the nearest degree, what is the maximum displacement of the pendulum?
d. The length
L
of a pendulum is related to the period
T
by the equation
T
−
2
π
L
g
, where
g
is the acceleration due to gravity. Find the length of the pendulum to the nearest meter
g
=
9.8
m
/
s
e
c
2
.
Find the value of f, correct to two decimal places.
Eratosthenes noticed that the shadow’s length was 1/8 the pole’s height. Suppose thepole’s height was ℎ = 2 and the shadow’s length was , = 0.25 . Calculate the anglebetween the Sun’s ray and the pole’s axis in degrees: - = XXXXXXXXXX . Expressthe same angle in radians: - = XXXXXXXXXX .1.7. Recall the beam of light travelling down the well in Syene. Extend that beam to thecenter of Earth. Also extend the pole’s axis to the center of Earth. These two extensionsare represented by dashed lines in Figure 1. The intersection of these two lines formsan angle . at the Earth’s center. Use basic geometry to find the relation between angles. and -. Calculate the angle . in radians: . = XXXXXXXXXX .
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