A cup spring balance of mass m1 undergoes vertical harmonic vibrations with an amplitude A (see Fig.). When the cup was in the lowest position somebody puts a weight of m in it. As a result, the vibrations ceased. Determine the initial period of oscillation (in sec.) of the cup. Take g = π2, m1 = 400 gm, m = 40 gm, A = 10 cm.

Engineering

Physics

Simple Harmonic Motion

Question

A cup spring balance of mass m₁ undergoes vertical harmonic vibrations with an amplitude A (see Fig.). When the cup was in the lowest position somebody puts a weight of m in it. As a result, the vibrations ceased. Determine the initial period of oscillation (in sec.) of the cup. Take g = π², m₁ = 400 gm, m = 40 gm, A = 10 cm.

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Original extreme = new mean

$\Rightarrow \frac{m_{1} g}{k} + A = \frac{(m_{1} + m)}{k} g$

$\Rightarrow \frac{mg}{k} = A$

$T = 2 π \sqrt{\frac{m_{1}}{k}} = 2 π \sqrt{\frac{m_{1} A}{mg}} = 2 \sec$

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