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Math Help - Shm :(

  1. #1
    Junior Member
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    Shm :(

    A point moves about O in SHM. The point has velocity v1 at distance x1 and velocity v2 at distance x2. Show that the period of motion is 2 * pi* sqrt[(x1^2-x2^2)/(v2^2-v1^2)].
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Sunyata View Post
    A point moves about O in SHM. The point has velocity v1 at distance x1 and velocity v2 at distance x2. Show that the period of motion is 2 * pi* sqrt[(x1^2-x2^2)/(v2^2-v1^2)].
    hi

    V_1^2=\omega ^2 (X_o^2-X_1^2) --- 1

    V_2^2=\omega ^2 (X_o^2-X_2^2) ---- 2

    2/1 \frac{V_2^2}{V_1^2}=\frac{X_o^2-X_2^2}{X_o^2-X_1^2}

    X_o^2=\frac{V_2^2X_1^2-V_1^2X_2^2}{V_2^2-V_1^2} --- 3

    Substitute into 1

    V_1^2=\omega ^2 (\frac{V_2^2X_1^2-V_1^2X_2^2}{V_2^2-V_1^2}-X_1^2)

    V_1^2=\omega ^2 (\frac{V_1^2X_1^2-V_1^2X_2^2}{V_2^2-V_1^2})

    \omega =\frac{2\pi}{T}

     <br />
T=\sqrt{\frac{4\pi^2(X_1^2-X_2^2)}{V_2^2-V_1^2}}<br />
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