In Section 14–5, the oscillation of a simple pendulum (Fig. 14–46) is viewed as linear motion along the are length x and analyzed via F = ma. Alternatively, the pendulum’s movement can be regarded as rotational motion about its point of support and analyzed using τ = Iα. Carry out this alternative analysis and show that θ ( t ) = θ max cos ( g l t + ϕ ) , where θ ( t ) is the angular displacement of the pendulum from the vertical at time t , as long as its maximum value is less than about 15°. FIGURE 14–46 Problem 92.
In Section 14–5, the oscillation of a simple pendulum (Fig. 14–46) is viewed as linear motion along the are length x and analyzed via F = ma. Alternatively, the pendulum’s movement can be regarded as rotational motion about its point of support and analyzed using τ = Iα. Carry out this alternative analysis and show that θ ( t ) = θ max cos ( g l t + ϕ ) , where θ ( t ) is the angular displacement of the pendulum from the vertical at time t , as long as its maximum value is less than about 15°. FIGURE 14–46 Problem 92.
In Section 14–5, the oscillation of a simple pendulum (Fig. 14–46) is viewed as linear motion along the are length x and analyzed via F = ma. Alternatively, the pendulum’s movement can be regarded as rotational motion about its point of support and analyzed using τ = Iα. Carry out this alternative analysis and show that
θ
(
t
)
=
θ
max
cos
(
g
l
t
+
ϕ
)
,
where θ(t) is the angular displacement of the pendulum from the vertical at time t, as long as its maximum value is less than about 15°.
FIGURE 14–46
Problem 92.
Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.
O 0.15 sec
In an oscillatory motion of a simple pendulum, the ratio of the maximum angular
acceleration, O"max, to the maximum angular velocity, O'max, is Tt s^(-1). What is
the time needed for the pendulum to complete two oscillations?
O 1 sec
O 2 sec
O 4 sec
O 0.5 sec
O 0.25 sec
A uniform disk has a pivot point P at the edge, if small oscillation has radius R = 15 cm, mass M = 1.0 kg, and the center of purcussion is how far from the pivot point (Ic.m. = (1/2) MR ^ (2) and give the answer in cm)
When a pendulum swings back and forth through a small arc, its horizontal displacement is given by D= A sin (t square root of 980 divided by L) where D is in cm, L is the length of the pendulum in cm, t is in seconds after passing the lowest point, and A is the maximum width the pendulum swings to the left and right.
If the length of a pendulum is 100cm, find the earliest time for wich the deisplacement is maximized.
How long is a clock pendulum that has a period of 1 sec. (This is the primary idea behind the classic grandfather clock.)
Chapter 14 Solutions
Physics for Scientists and Engineers with Modern Physics
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