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28 June, 08:36

find a model for simple harmonic motion if the position at t = 0 is 6, the amplitude is 6 centimeters, and the period is 4 seconds

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  1. 28 June, 09:19
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    y = 6cos (π/2) t

    Step-by-step explanation:

    Given in the question that,

    in a simple harmonic motion in which

    at t=0 the amplitude is 6 cm, so the simple harmonic motion will be in cosine form. As in case of sine function, the value of function at t=0 is 0.

    And,

    the period is given as 4 sec

    We know that model equation of simple harmonic motion is

    y = a. cosb (t + c) + d

    here,

    a is amplitude

    c is Horizontal shift or phase shift

    d is Vertical shift

    Step1Find b

    Period = 2 π / b

    4 = 2π / b

    b = 2π/4

    b = 1π/2

    Step2Find shifts

    Horizontal and vertical shifts are 0.

    So, c = 0 and d = 0

    Step3Plug those values in the above in the equation

    y = 6cos π/2 (t + 0) + 0

    y = 6cos (π/2) t
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