Find the 53rd term of the arithmetic sequence
1 answer:
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Answer:
The equation of the displacement as a function of time
is :
Step-by-step explanation:
Generally , A simple harmonic wave is a sinusoidal function that is it can be expressed in simple or
terms.
Thus,
is the general form of displacement of a SHM.
where,
- <em>
is the displacement with respect to the mean position at any time
</em>
- <em>
is amplitude </em>
- <em>
is the natural frequency of oscillation (
)</em>
- <em>
is the phase angle which indicates the initial position of the object in SHM (
)</em>
given,
- Time period (
) =
- The natural frequency (
∴
=
∴
the equation :
<em>⇒ </em> ------1
since when
,
<em>⇒ ------2</em>
where n is an integer ;
<u>⇒since the bouy immediately moves in the negative direction , must be negative or c must be an odd multiple of
.</u>
<em>⇒ ------3</em>
where k is also an integer ;
the least value of ;
thus ,
the equation is :
<em></em>
First, convert that into a y=mx+b form.
Move the x to the other side so y is the only thing on the left. Since you moved it to the other side of the equal sign, be sure to make that number negative (the opposite sign)
Now… you have 4y=-3x+28
Let’s get y by itself. Since you’re multiplying 4 and y, you divide everything by 4 to get your y.
That leaves you with y=-3/4x+7.
We are looking at slope, which is your m in the y=mx+b form.
That is -3/4. The answer is the last square.
Move the x to the other side so y is the only thing on the left. Since you moved it to the other side of the equal sign, be sure to make that number negative (the opposite sign)
Now… you have 4y=-3x+28
Let’s get y by itself. Since you’re multiplying 4 and y, you divide everything by 4 to get your y.
That leaves you with y=-3/4x+7.
We are looking at slope, which is your m in the y=mx+b form.
That is -3/4. The answer is the last square.