Question

A 696 g mass is hung on a spring. As a result the spring stretches 22.5 cm. If the object is then pulled an additional 3.00 cm downward and released, what is the period of the resulting oscillation? Give your answer in seconds with 3 significant figures.

Answer 1

First, find the spring constant of the spring

Given that the spring stretches 22.5cm when a mass of 696g is hung on it.

Use Hooke's Law $F=kx$

Here Force is the weight of the mass

$W=kx$

$mg=kx$

$\frac{mg}{x}=k$

$\frac{0.696kg*9.81m/s^{2}}{0.225m}=k$

${\color{Red} k=30.3456N/m}$

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Time Period, $T=2\pi \sqrt{\frac{m}{k}}$

$T=2\pi \sqrt{\frac{0.696kg}{30.3456N/m}}$

ANSWER: ${\color{Red} T=0.952s}$

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