Ii) When the number of springs in parallel increases, the effective stiffness (spring constant) of the system increases. Since frequency is directly proportional to the square root of the stiffness

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ii) When the number of springs in parallel increases, the effective stiffness (spring constant) of the system increases. Since frequency is directly proportional to the square root of the stiffness (f∝kf \propto \sqrt{k}), an increase in stiffness leads to an increase in the frequency of oscillation of the system.

iii)

  1. State Hooke's Law, which relates force, spring stiffness, and extension.

    F=keF = ke

    where FF is the force (weight), kk is the spring stiffness, and ee is the extension.

  2. Substitute the given values into the formula.

    Given: F=8.0 NF = 8.0 \text{ N} and k=125 Nm−1k = 125 \text{ Nm}^{-1}.

    8.0 N=(125 Nm−1)×e8.0 \text{ N} = (125 \text{ Nm}^{-1}) \times e

  3. Solve for the extension, ee.

    e=8.0 N125 Nm−1e = \frac{8.0 \text{ N}}{125 \text{ Nm}^{-1}} e=0.064 me = 0.064 \text{ m}

    The extension of the spring is 0.064 m\boxed{\text{0.064 m}}.

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