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4 November, 16:14

The position of an object connected to a spring varies with time according to the expression x (5.2 cm) sin (8.0 pt). Find (a) the period of this motion, (b) the frequency of the motion, (c) the amplitude of the motion, and (d) the fi rst time after t 0 that the object reaches the position x 2.6 cm.

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  1. 4 November, 16:24
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    A. Period (T) = 0.25rad/s

    B. Frequency (f) = 4.0hz

    C. Amplitude (A) = 5.2cm

    D. Time (t) = 0.6256secs

    Explanation:

    A. Firstly, we Compare the equation

    x = (5.2 cm) sin (8.0π t)

    with

    x=Asin (ωt) (General equation)

    Then

    ω = 2πt

    => T=2π / ω =

    = 2 π/8.0π=0.25rad/s

    B. frequency (f) = 1/T

    = 1/0.25

    = 4.0hz

    C. A = 5.2 cm by comparison with the general equation.

    D. x = Asin (ωt)

    2.6 = 5.2sin (8.0π t)

    sin (8.0π t) =

    2.6/5.1 = 0.5098

    (8.0π t) = sin⁻¹0.5098 = 30.650

    t = 30.650/8.0π

    t = 0.6256secs
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