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16 June, 07:11

A horizontal mass-spring system is in SHM. The mass is 0.25kg, the spring constant is 15N/m, and the amplitude is 20cm. a) What is the maximum speed of the mass and where does it occur? b) What is its speed at the 1/2 amplitude position of its motion?

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  1. 16 June, 09:01
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    maximum speed = 1.55 m/s

    speed is 0.775 m/s

    Explanation:

    given data

    mass m = 0.25 kg

    spring constant k = 15 N/m

    amplitude A = 20 cm = 0.2 m

    to find out

    maximum speed and speed at the 1/2 amplitude

    solution

    we know formula for maximum speed that is

    maximum speed = amplitude * √ (k/mass)

    put all value

    maximum speed = 0.2 * √ (15/0.25)

    maximum speed = 1.55 m/s

    and

    at the 1/2 amplitude

    we apply here conservation of energy that is

    1/2 * m*v² = 1/2 * k*x²

    here we know x = A/2 that is 20 / 2 = 10 cm = 0.1 m

    so

    0.25 v² = 15 * 0.1²

    v² = 0.600625

    v = 0.775

    so speed is 0.775 m/s
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