In the following question, a figure carrying certain
numbers is given. Assuming that the numbers in
the figure follow a similar pattern, find the missing
number.
17
8
5
13
7
alular
4
6
12
3
10
6
4
?
Answers
Answer:
Step-by-step explanation:
Answer given in option as well as in figure is incorrect.
the correct logic is
915 - 364 = 551
and 789 - 543 = 246
Similarly, 863 - 241 = 622.
Answer:
24
Step-by-step explanation:
A simple pendulum consists of a ball (point-mass) m hanging from a (massless) string of length L and fixed at a pivot point P. When displaced to an initial angle and released, the pendulum will swing back and forth with periodic motion. By applying Newton's secont law for rotational systems, the equation of motion for the pendulum may be obtained
τ
=
I
α
⇒
−
m
g
sin
θ
L
=
m
L
2
d
2
θ
d
t
2
and rearranged as
d
2
θ
d
t
2
+
g
L
sin
θ
=
0
If the amplitude of angular displacement is small enough, so the small angle approximation ($\sin\theta\approx\theta$) holds true, then the equation of motion reduces to the equation of simple harmonic motion
d
2
θ
d
t
2
+
g
L
θ
=
0
The simple harmonic solution is
θ
(
t
)
=
θ
o
cos
(
ω
t
)
,
where
θ
o
is the initial angular displacement, and
ω
=
√
g
/
L
the natural frequency of the motion. The period of this sytem (time for one oscillation) is
T
=
2
π
ω
=
2
π
√
L
g
.
Small Angular Displacements Produce Simple Harmonic Motion
The period of a pendulum does not depend on the mass of the ball, but only on the length of the string. Two pendula with different masses but the same length will have the same period. Two pendula with different lengths will different periods; the pendulum with the longer string will have the longer period.
How many complete oscillations do the blue and brown pendula complete in the time for one complete oscillation of the longer (black) pendulum?
From this information and the definition of the period for a simple pendulum, what is the ratio of lengths for the three pendula?
With the assumption of small angles, the frequency and period of the pendulum are independent of the initial angular displacement amplitude. A pendulum will have the same period regardless of its initial angle. This simple approximation is illustrated in the animation at left. All three pendulums cycle through one complete oscillation in the same amount of time, regardless of the initial angle.