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11 June, 23:21

The function x = (7.8 m) cos[ (5πrad/s) t + π/3 rad] gives the simple harmonic motion of a body. At t = 4.4 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion?

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  1. 12 June, 02:41
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    a. 3.84m

    b.-106.67m/s

    c. 947.3m/s^2

    d. 70.17 rad

    e. 2.5Hz

    d. 0.4secs

    Explanation:

    Given x = (7.8) cos[5πrad/s) t+π/3) ]

    a. Displacement at t=4.4

    7.8cos (5π*4.4+π/3) = 3.84m

    b. velocity

    V = dx/dr=-5π (7.8) sin (5πrad/s) t+π/3

    at t=4.4

    -5π (7.8) sin (5π*4.4+π/3) = -106.67m/s

    c. acceleration

    a=d^2x/dr^2

    - (5π) ^2 (7.8) cos (5π*t+π/3)

    at t=4.4

    - (5π) ^2 (7.8) cos (5π*4.4+π/3) = -947.3m/s^2

    d. Phase = (5πrad/s) t+π/3

    At t=4.4

    5π*4.4+π/3=70.17 rad

    e. frequency

    Given x = 7.8cos (5πt+π/3

    Compare with x=Acos (2πft)

    2πft=5πt

    F=2.5Hz

    f. T=1/f

    T=1/2.5=0.4sec
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