Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

A weight is suspended from a spring and is moving up and down in a simple harmonic motion . At start , the weight is pushed up 12 cm above the resting position , and then released . After 26 seconds , the weight reaches again to its highest position Find the equation of the motion , and locate the weight with respect to the resting position after 25 seconds since it was released
​

Sagot :

xero099

The weight is 11.651 centimeters above the resting position.

Procedure - Postion formula for a weight under simple harmonic motion

Simple harmonic motion model

Mathematically speaking, a simple harmonic motion is described by the following formula:

[tex]y = A\cdot \cos \left(\frac{2\pi\cdot t}{T}) + y_{o}[/tex] (1)

Where:

  • [tex]t[/tex] - TIme, in seconds.
  • [tex]T[/tex] - Period, in seconds.
  • [tex]A[/tex] - Amplitude, in centimeters.
  • [tex]y_{o}[/tex] - Resting position, in centimeters.

Current position of the weight with respect to the resting position

Please notice that the period is the time needed by the weight to complete one cycle. If we know that [tex]A = 12\,cm[/tex], [tex]y_{o} = 0\,cm[/tex], [tex]T = 26\,s[/tex] and [tex]t = 25\,s[/tex], then the current position of the weight is:

[tex]y = 12\cdot \cos \left(\frac{2\pi\cdot 25}{26} \right)+0[/tex]

[tex]y = 11.651\,cm[/tex]

The weight is 11.651 centimeters above the resting position. [tex]\blacksquare[/tex]

To learn more on simple harmonic motion, we kindly invite to check this verified question: https://brainly.com/question/17315536

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.