A 1.35 kgkg block is attached to a spring with spring constant 15.0 N/mN/m . While the block is sitting at rest, a student hits it with a ha

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A 1.35 kgkg block is attached to a spring with spring constant 15.0 N/mN/m . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 34.0 cm/scm/s . What are

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  1. Given :

    Mass of block , m = 1.35 kg .

    Speed constant , k = 15 N/m .

    Speed at centre , v = 34 cm/s = 0.34 m/s .

    To Find :

    The amplitude of oscillation .

    Solution :

    Now , we know total energy is conserved in SHM .

    So , K.E at zero displacement :

    [tex]K.E=\dfrac{mv^2}{2}\\\\K.E=\dfrac{1.35\times 0.34^2}{2}\\\\K.E=7.8\times 10^{-2}\ J[/tex]

    Now , this K.E is equal to maximum P.E :

    [tex]P.E=K.E=7.8\times 10^{-2}\ J[/tex] .

    [tex]P.E=\dfrac{kA^2}{2}\\\\7.8\times 10^{-2}=\dfrac{kA^2}{2}\\\\A=\sqrt{\dfrac{2\times 7.8 \times 10^{-2}}{15}}\ m\\\\A=0.1019 \ m\\\\A=10.2\ cm[/tex]

    Therefore , the amplitude is 10.2 cm .

    Hence , this is the required solution .

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