Two masses are executing SHM under influence of a vertical spring as shown with an amplitude of 2cm and angular frequency of 5 rad/s. When the extension of spring is maximum, suddenly the string breaks and 3kg mass falls off. What is the maximum velocity of the 1kg mass (in cm/s) during subsequent motion ?

Engineering

Physics

Newtons Second Law of Motion

SHM of Spring Block System

Basics of Simple Harmonic Motion

Question

Two masses are executing SHM under influence of a vertical spring as shown with an amplitude of 2cm and angular frequency of 5 rad/s. When the extension of spring is maximum, suddenly the string breaks and 3kg mass falls off. What is the maximum velocity of the 1kg mass (in cm/s) during subsequent motion ?

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$x_{i} = A + \frac{4 g}{k} = 42 cm, K = {mω}^{2} = (4) (5)^{2} = 100 N / m$

${x_{0}}^{'} = \frac{1 g}{k} = 10 cm$

$A_{new} = 42 - 10 = 32 cm, ω_{new} = \sqrt{\frac{K}{1 kg}} = 10 rad / s$

$v_{max} = A_{new} ω_{new} = 320 cm / \sec$