An object moves up and down the y-axis with an acceleration given as a function of time t by the expression a = a sin ω t, where a and ω are constants. what is the period of this motion?

The period of this motion is T = 2pi/w

Acceleration = A = asin(wt)

To calculate the velocity, integration over time is done which results in

V = -a ₓ cos(wt)/w

Integration is done again to get the movement which results in

P = -asin(wt)/w²

Note that sin and cos are 2×pi where pi = 3.14159 periodic. We can infer

that sin(0) = sin(2pi)

The period of the function: P = -asin(wt)/w²

sin( 0 ) is when t = 0, and sin(2*pi) is when t = 2*pi/w

The period of motion is T = 2pi/w .

Read more about Period here link

T = 2*pi/w

Explanation: We know that the acceleration of the object is:

A = a*sin(wt)

Now, if we want to obtain the velocity, we must integrate over time, then we get:

V = -a*cos(wt)/w

We integrate again to get the movement:

P = -a*sin(wt)/w^2

(you can see that the trigonometric equations never vanish)

Now, as you may know that sin and cos are 2*pi (where pi = 3.141592653...) periodic, this means that:

sin(0) = sin(2*pi)

Then the period of the function: P = -a*sin(wt)/w^2

sin( 0 ) is when t = 0, and sin(2*pi) is when t = 2*pi/w

Then the period of motion is T = 2*pi/w .

as we probably am aware that our atmosphere or air have various levels, each level has different gasses, and each gas has another porousness. at the point when the light originates from lower porousness to higher penetrability, it alters its course. with the goal that implies that when the light originates from the moon to the earth, it alters it's course a lot more occasions. it essentially implies that the state of the light piece of the moon is changed on the earth.

not copied too! hope this !

joke:

h o h o hope you have a merry christmas!