Suppose a radio signal (light) travels from Earth and through space at a speed of 3 × 10^8/ (this is the speed of light in vacuu
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The image of the triangle is to be formed by rotating ΔXYZ 180 degrees about the (2, -3) as shown in the graph.
<h3>What is Geometry?</h3>It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Triangle XYZ has vertices X(0, 2), Y(4, 4), and Z(3, –1).
If the triangle is ΔXYZ. Then the image of the triangle is to be formed by rotating ΔXYZ 180 degrees about the (2, -3) as shown in the graph.
More about the geometry link is given below.
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Explanation:
A) To prove the motion of the center of mass of the cylinders is simple harmonic:
System diagram for given situation is shown in attached Fig. 1
We can prove the motion of the center of mass of the cylinders is simple harmonic if
where aₓ is acceleration when attached cylinders move in horizontal direction:
<h3>PROOF:</h3>rotational inertia for cylinders is given as:
-----(1)
Newton's second law for angular motion is:
∑τ = Iα ------(2)
For linear motion in horizontal direction it is:
∑Fₓ = Maₓ ------ (3)
By definition of torque:
τ = RF --------(4)
Put (4) and (1) in (2)
from Fig 3 it can be seen that fs is force by which the cylinders roll without slipping as they oscillate
So above equation becomes
------ (5)
As angular acceleration is related to linear by:
Eq (5) becomes
---- (6)
aₓ shows displacement in horizontal direction
From (3)
∑Fₓ = Maₓ
Fₓ is sum of fs and restoring force that spring exerts:
----(7)
Put (7) in (3)
[/tex] -----(8)
Using (6) in (8)
--- (9)
For spring mass system
----- (10)
Equating (9) and (10)
then (9) becomes
(The minus sign says that x and aₓ have opposite directions as shown in fig 3)
This proves that the motion of the center of mass of the cylinders is simple harmonic.
<h3 /><h3>B) Time Period</h3>Time period is related to angular frequency as:
