A load of mass m falls from a height h on to the scale pan hung from a spring, as shown in the figure. If the spring constant is k , mass of the scale pan is zero and the mass m does not bounce, relative to the pan, then the amplitude of vibration is

Question

A load of mass m falls from a height h on to the scale pan hung from a spring, as shown in the figure. If the spring constant is k , mass of the scale pan is zero and the mass m does not bounce, relative to the pan, then the amplitude of vibration is, m g k, m g k 1 + 2 h k m g, m g k + m g k 1 + 2 h k m g, m g k 1 + 2 h k m g - m g k

MARKS App · Accepted Answer

According to conservation principle, m g h = 1 2 k x 0 2 - m g x 0 where x 0 is maximum elongation in spring (when particle is in its lowest extreme position) or 1 2 k x 0 2 - m g x 0 - m g h = 0 or x 0 2 - 2 m g k x 0 - 2 m g k h = 0 ∴ x 0 = 2 m g k ± 2 m g k 2 + 4 × 2 m g k h 2 ∵ Amplitude = elongation in spring for lowest extreme position - elongation in spring for equilibrium position = x 0 - x 1 = m g k 1 + 2 h k m g

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