The motion of the mass as it moves on the bottom of the spring is a
repetitive motion.
Reasons:
The general form of the equation of the simple harmonic motion of the
mass is <em>d</em> = a·sin(ω·t)
Where;
d = The distance of the mass from the rest position
a = The maximum displacement of the mass from the equilibrium position = 6 cm
ω = The frequency of rotation
t = The time of motion
ω = The frequency of rotation
![\displaystyle \omega = \mathbf{\frac{2 \cdot \pi}{T}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Comega%20%3D%20%5Cmathbf%7B%5Cfrac%7B2%20%5Ccdot%20%5Cpi%7D%7BT%7D%7D)
Where;
T = The time to complete one cycle (the period of oscillation) = 4 seconds
![\displaystyle \omega = \frac{2 \cdot \pi}{4} = \frac{\pi}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Comega%20%3D%20%5Cfrac%7B2%20%5Ccdot%20%5Cpi%7D%7B4%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D)
Combining the above values gives the modelling equation as follows;
![\displaystyle d = 6 \cdot sin\left(\frac{\pi}{2} \cdot t \right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%206%20%5Ccdot%20sin%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7D%20%5Ccdot%20t%20%5Cright%29)
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Answer:
a=8, -8
Step-by-step explanation:
a^2-15=49
a^2=49+15
a^2=64
a=sqrt(64)
a=8, -8
Answer:
Angle 4 also has a measurement of 34 degrees because opposite angles of intersecting lines are congruent. In other words, angles 2 and 4 are congruent, so are angles 1 and 3.
I believe the remainder would be 5.
Hope this helps!
Lets say that J is for Jennys messages, B is for Boris’ and E is for Erics (or Ericas?).
79 = J + B + E
J = E - 6
B = 3E
Since both Jenny’s and Boris’ number of text messages has some kind of relation to Eric’s number of messages, we can say that:
79 = E - 6 (Jenny) + 3E (Boris) + E (Eric), so:
79 = E - 6 + 3E + E /combine like terms
79 = 5E - 6 /add 6 to both sides
79 + 6 = 5E /switch sides + combine like terms
5E = 85 /divide both sides by 5
E = 85/5
E = 17
So, Eric sent 17 messages. Lets get back to those equations we made for Jenny and Boris:
J = E - 6 = 17 - 6 = 11
B = 3E = 3 * 17 = 51
And we can check if it adds up: 51 + 11 + 17 = 79, which is what we were supposed to get.