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4 September, 18:10

A mass m1 is hung from a spring oscillates on a spring with spring constant k1. The amplitude of its motion is A1 and it has a maximum magnitude acceleration a1. If the mass is doubled, the spring constant tripled, and the amplitude quadrupled, what will the new maximum magnitude acceleration be?

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  1. 4 September, 20:12
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    the new acceleration will be six times the initial acceleration

    Explanation:

    A mass m1 is hung from a spring oscillates on a spring with spring constant k1. The amplitude of its motion is A1 and it has a maximum magnitude acceleration a1. If the mass is doubled, the spring constant tripled, and the amplitude quadrupled, what will the new maximum magnitude acceleration be

    mass = m1 acceleration

    f=force applied

    k=force constant

    x=extension. amplitude or compression

    a=

    from hooke's law we know that the force exerted on an elastic material is directly proportional to the extension provided that the elastic limit is not exceeded

    f=kx

    m*a=k*x

    a1=kx/m1

    m2=2m1

    k2=3k1

    x2=4x1

    substituing into the initial equation

    a2=3k1*4x1/2m1

    a2=6k1x1/m1

    a2=6a1

    the new acceleration will be six times the initial acceleration
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