A mass m 1 = 1 kg connected to a horizontal spring performs S.H.M. with amplitude A . While mass m 1 is passing through mean position another mass m 2 = 3 kg is placed on it so that both the masses move together with amplitude A 1 . The ratio of A 1 A is p q 1 2 , where p and q are the smallest integers. Then what is the value of p + q ?

Question

A mass m 1 = 1 kg connected to a horizontal spring performs S.H.M. with amplitude A . While mass m 1 is passing through mean position another mass m 2 = 3 kg is placed on it so that both the masses move together with amplitude A 1 . The ratio of A 1 A is p q 1 2 , where p and q are the smallest integers. Then what is the value of p + q ?,

MARKS App · Accepted Answer

P.E of the oscillating mass is given by E = 1 2 m ω x 2 = 1 2 k x 2 where k = m ω 2 Let k = m ω 2 be the velocity at mean position. When mass M 2 is attached v 2 = m 1 v 1 m 1 + m 2 If A 1 be the new amplitude 1 2 k A 1 2 = 1 2 ( m 1 + m 2 ) v 2 2 = 1 2 k A 2 × m 1 m 1 + m 2 ⇒ A 1 A = m 1 m 1 + m 2 = 1 4

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