Question

# A spring is hanging vertically from a shelf. When a weight of mass 0.16 kg is...

A spring is hanging vertically from a shelf. When a weight of mass 0.16 kg is hung from the spring, the spring stretches a distance 25 cm. That weight is then removed and a new weight of mass 0.30 kg is hung from the spring. This second weight is then lifted a distance of 1.8 cm and released. The weight oscillates up and down. What is the period of oscillation (in units of seconds)?

For the hung mass 0.16 kg:

This mass experiences 2 vertical forces:

i) Gravitational force = mg downwards, where m is mass and g is gravitational acceleration.

ii) Sprinf force=kx upwards, where k is spring constant and x is elongation.

For equilibrium, kx=mg

=>k=mg/x.

Here,m=0.16 kg and x=25 cm = 0.25 m.

So,k=0.16*9.8/0.25 = 6.272 N/m.

For the mass 0.30 kg:

Period of oscillation is given by:2(m/k)^0.5

Here,m=0.30 kg and k = 6.272 N/m.

So, period of oscillation=2(0.30/6.272)^0.5 = 1.374 seconds.

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