(a) (b) (c) (d) The figure below shows a pendulum with length L and the angle 0 from the vertical to the pendulum. It can be shown that 0, as a function of time, satisfies the following nonlinear differential equation where g d²0 g dt² denotes the acceleration due to gravity. + - sin 0 = 0 For small values of 0 we can assume de dt 0 sin 0 L such that the differential equation can be considered to be linear. Find the equation of motion of the pendulum with length 750 cm if 0 is initially 15° and its initial angular velocity is = 1 rad/s. What is the maximum angle from the vertical? What is the period of the pendulum (the time to complete one back-and-forth swing)? When will the pendulum be vertical from initial position, that is, 0 = 0 ?
(a) (b) (c) (d) The figure below shows a pendulum with length L and the angle 0 from the vertical to the pendulum. It can be shown that 0, as a function of time, satisfies the following nonlinear differential equation where g d²0 g dt² denotes the acceleration due to gravity. + - sin 0 = 0 For small values of 0 we can assume de dt 0 sin 0 L such that the differential equation can be considered to be linear. Find the equation of motion of the pendulum with length 750 cm if 0 is initially 15° and its initial angular velocity is = 1 rad/s. What is the maximum angle from the vertical? What is the period of the pendulum (the time to complete one back-and-forth swing)? When will the pendulum be vertical from initial position, that is, 0 = 0 ?
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Transcribed Image Text:(a)
(b)
(c)
(d)
The figure below shows a pendulum with length L and the angle 0 from the
vertical to the pendulum. It can be shown that 0, as a function of time, satisfies
the following nonlinear differential equation
d²0 g
dt² L
where g denotes the acceleration due to gravity.
+ sin 0 0
For small values of 0 we can assume
de
dt
A
0 sin 0
L
such that the differential equation can be considered to be linear.
Find the equation of motion of the pendulum with length 750 cm if 0 is initially
15° and its initial angular velocity is
= 1 rad/s.
What is the maximum angle from the vertical?
What is the period of the pendulum (the time to complete one back-and-forth
swing)?
When will the pendulum be vertical from initial position, that is, 0 = 0 ?
Transcribed Image Text:(e)
(f)
What is the angular velocity when the pendulum is vertical?
Describe how the pendulum concept is used in the pendulum clock.
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