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A weight hangs from a spring attached to a ceiling, and the weight moves up and down. The table shows the distance in centimeters, y, between the weight and the ceiling after x seconds.

A 2-column table with 5 rows. Column 1 is labeled x with entries 0, 0.25, 0.5, 0.75, 1. Column 2 is labeled y with entries 19, 22.5, 19. 15.5, 19.

Which equation represents the distance between the weight and the ceiling?

y = 7 sine (pi x) + 19
y = 7 sine (2 pi x) + 19
y = 3.5 sine (pi x) + 19
y = 3.5 sine (2 pi x) + 19)

A weight hangs from a spring attached to a ceiling and the weight moves up and down The table shows the distance in centimeters y between the weight and the cei class=

Respuesta :

Option D is the correct answer

y = 3.5 sine (2 pi x) + 19)

The correct answer to the problem is y = 3.5 sin ( ( 2 pi x ) + 19 ).

  • Simple Harmonic motion is an oscillatory motion of constant Amplitude and of a single frequency.
  • It acts under a restoring force ' F',  which is directly proportional to the displacement ' x ' from the mean position and always acts towards the mean position, F = - K x¹, Where K is constant.
  • We can express the Simple Harmonic motion as
  • x = A sin (ωt + φ)
  • Where,
  • displacement
  • from the mean position is x , φ is the
  • initial phase
  • , and A is the
  • Amplitude.
  • Amplitude is the maximum Displacement measured from the mean position.
  • The particle's maximum displacement will always be after T/4 time after the mean position.

We can quickly determine from the table that the mean position is at 19 cm from the ceiling as it is at 19 cm from the ceiling when the time is 0 sec, and the Amplitude is 3.5 as it is the maximum displacement from the mean position after T/4 second is 3.5 cm.

Now, we have Amplitude as 3.5 and the initial position at 19.

Now, we know that ω = 2π / T

But T is 1 sec in our case as the particle is taking 1 second to complete 1 oscillation,

So ω will become 2π.

so our equation will become after putting the values of Amplitude and initial position and ω as 2π ,

x = 3.5 sin ( 2π t + 19 )

but in question, they have denoted displacement as ' y ' and time as ' x '

So our final equation will become

y = 3.5 sin ( 2π x + 19 )

Hence, our final solution to the question is that the particle will perform Simple Harmonic Motion, and the equation of that will be

y = 3.5 sin ( 2 pi x + 19 )

where y is denoted as displacement and x is denoted as time.

Learn more about Simple Harmonic Motion (SHM) here:

https://brainly.com/question/24646514

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