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State I. the two characteristics of oscillatory motion. II. two examples of bodies exhibiting oscillatory motion. A body of mass 0.5 kg is suspended vertically on a spiral spring. If the extension produced is 0.2 m, calculate the force constant of the spring.

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b)i)
I. The two characteristics of oscillatory motion are:

  • It is a periodic motion, meaning it repeats itself after a fixed interval of time.
  • It is a to-and-fro motion about a fixed equilibrium position.

II. Two examples of bodies exhibiting oscillatory motion are:

  • A simple pendulum swinging.
  • A mass suspended from a spring oscillating vertically.

b)ii)

  1. Calculate the force (weight) exerted by the mass on the spring.

    The force FF is equal to the weight of the mass, which is given by F=mgF = mg.

    F=0.5 kg×10 m/s2F = 0.5\, \text{kg} \times 10\, \text{m/s}^2 F=5 NF = 5\, \text{N}

  2. Use Hooke's Law to calculate the force constant of the spring.

    Hooke's Law states F=kxF = kx, where FF is the force, kk is the force constant, and xx is the extension.
    Rearranging for kk:

    k=Fxk = \frac{F}{x}

    Substitute the values:

    k=5 N0.2 mk = \frac{5\, \text{N}}{0.2\, \text{m}} k=25 N/mk = 25\, \text{N/m}

    The force constant of the spring is:

    25 N/m\boxed{25\, \text{N/m}}
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