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A spring stretches 3.5 cm when a 9 g object is hung from it. The object is replaced with a block of mass 26 g which oscillates in simple harmonic motion. Calculate the period of motion. The acceleration of gravity is 9.8 m/s 2.

Answer :

Answer:

The period of motion  of new mass T = 0.637 sec

Explanation:

Given data

Mass of object (m) = 9 gm = 0.009 kg

Δx = 3.5 cm = 0.035 m

We know that spring force is given by

F = m g

F = 0.009 × 9.81 = 0.08829 N

Spring constant

[tex]k = \frac{F}{x}[/tex]

[tex]k = \frac{0.08829}{0.035}[/tex]

k = 2.522 [tex]\frac{N}{m}[/tex]

New mass[tex](m_1)[/tex] = 26 gm = 0.026 kg

Now the period of motion is given by

[tex]T = 2 \pi \sqrt{\frac{m}{k} }[/tex]

[tex]T = 2 \pi \sqrt{\frac{0.026}{2.522} }[/tex]

T = 0.637 sec

This is the period of motion  of new mass.

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