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A mass of 0.90 kg is suspended from the lower end of a light spring of stiffness 80 N m<sup>-1</sup> - AQA - A-Level Physics - Question 25 - 2020 - Paper 1

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A mass of 0.90 kg is suspended from the lower end of a light spring of stiffness 80 N m<sup>-1</sup>. When the mass is displaced vertically and released, it undergoe... show full transcript

Worked Solution & Example Answer:A mass of 0.90 kg is suspended from the lower end of a light spring of stiffness 80 N m<sup>-1</sup> - AQA - A-Level Physics - Question 25 - 2020 - Paper 1

Step 1

Calculate the angular frequency

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Answer

The angular frequency (ω\omega) of a mass-spring system is given by the formula:

ω=km\omega = \sqrt{\frac{k}{m}}

where:

  • k=80N m1k = 80 \, \text{N m}^{-1} (stiffness of the spring)
  • m=0.90kgm = 0.90 \, \text{kg} (mass)

Substituting in the values, we get:

ω=800.90=88.899.43rad s1\omega = \sqrt{\frac{80}{0.90}} = \sqrt{88.89} \approx 9.43 \, \text{rad s}^{-1}

Step 2

Convert angular frequency to frequency

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Answer

The frequency (ff) can be calculated from the angular frequency using the formula:

f=ω2πf = \frac{\omega}{2\pi}

Substituting the value of ω\omega:

f=9.432π9.436.281.50Hzf = \frac{9.43}{2\pi} \approx \frac{9.43}{6.28} \approx 1.50 \, \text{Hz}

Step 3

Conclusion

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Answer

Thus, the frequency of the oscillations is approximately 1.50 Hz. The correct answer is C.

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