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Math Help - Word problem? sin and cos....please help!? im stuck

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    Word problem? sin and cos....please help!? im stuck

    Ive been trying to solve this problem for 2 hours now..

    Suppose a weight is set in motion from a position 3 centimeters below the equilibrium position and with a downward velocity of 4 centimeters per second. (please note that the vertical number line used for position is upside down. This is a conversion from physics and it means that position below equilibrium actually correspond to a positive value.) Assume that spring stiffness and mass of the weight mean that w=2 for this system.


    Write the function x(t) that gives the position of the weight as a function of time t in seconds. (Your function should consist of a sine term and a cosine term)
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    Re: Word problem? sin and cos....please help!? im stuck

    Quote Originally Posted by agape801 View Post
    Ive been trying to solve this problem for 2 hours now..

    Suppose a weight is set in motion from a position 3 centimeters below the equilibrium position and with a downward velocity of 4 centimeters per second. (please note that the vertical number line used for position is upside down. This is a conversion from physics and it means that position below equilibrium actually correspond to a positive value.) Assume that spring stiffness and mass of the weight mean that w=2 for this system.


    Write the function x(t) that gives the position of the weight as a function of time t in seconds. (Your function should consist of a sine term and a cosine term)
    x(t) = A\sin(\omega t + \phi)

    at t = 0 ...

    3 = A\sin{\phi}

    v(t) = A\omega \cos(\omega t + \phi)

    at t = 0 ...

    4 = 2A\cos{\phi}

    from the two equations ...

    \frac{3}{2} = \tan{\phi}

    \phi = \arctan\left(\frac{3}{2}\right)

    3 = A\sin\left[\arctan\left(\frac{3}{2}\right)\right]

    3 = A \cdot \frac{3}{\sqrt{13}}

    A = \sqrt{13}

    x(t) = \sqrt{13} \sin(2t + \phi)

    x(t) = \sqrt{13}\left[\sin(2t)\cos{\phi} + \cos(2t)\sin{\phi}\right]

    x(t) = \sqrt{13}\left[\sin(2t) \cdot \frac{2}{\sqrt{13}} + \cos(2t) \cdot \frac{3}{\sqrt{13}}\right]

    x(t) = 2\sin(2t) + 3\cos(2t)

    graph of position and velocity attached ...
    Attached Thumbnails Attached Thumbnails Word problem? sin and cos....please help!? im stuck-shmgraf.jpg  
    Thanks from agape801
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