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A package is oscillating on a spring scale with a period of 5.00 s. at time t = 0.00 s the package has zero speed and is at x = 8.50 cm. at what time after t = 0.00 s will the package first be at x = 4.50 cm?

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Under the assumption of simple harmonic motion, the package will be at x = 4.50 centimeters at a time of 0.805 seconds.

How to analyze an object on simple harmonic motion

Simple harmonic motion is a kind of periodic motion represented by sinusoidal functions. Physically speaking, it is a good approximation for periodic motion due to small perturbations and with absence of frictions and viscous forces on the system.

The position of an object under simple harmonic motion is described by the following equation:

x (t) = A · cos (2π · t / T + Ф)      (1)

Where:

  • A - Amplitude, in centimeters
  • T - Period, in seconds
  • Ф - Angular phase, in radians
  • x(t) - Position, in centimeters

If we know that T = 5 s, A = 8.50 cm, Ф = 0 rad and x = 4.50 cm, then the time when the package will reach x = 4.50 cm is:

4.50 = 8.50 · cos (2π · t / 5)

9 / 17 = cos (2π · t / 5)

0.322π = 2π · t / 5

t = 0.805 s

Under the assumption of simple harmonic motion, the package will be at x = 4.50 centimeters at a time of 0.805 seconds.

To learn more on simple harmonic motion: https://brainly.com/question/17315536

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