GATE 2007 AEROSPACE ENGINEERING (Q 21-30)

  1. A 1 kg mass attached to a spring elongates it by 16 mm. The mass is then pulled from its equilibrium position by 10 mm and released from rest. Assuming the acceleration due to gravity of 9.81 m/s2, the response of the mass is given by
    1. x = 10sin24.76t
    2. x = 10cos24.76t
    3. x = sin16t
    4. x = 10cos16t

    Answer:- 10cos24.76t
    A = 10 mm
    l = 16 mm
    ω = (g/l)0.5 = (9.8/0.016)0.5 = 24.76 rad/s2
    When t = 0, x = 10 =A
    Therefore, x = Acosωt = 10cos24.76t

  2. A spring-mass-damper system is excited by a force F0sinωt. The amplitude at resonance is measured to be 1 cm. At half the resonance frequency, the amplitude is 0.5 cm. The damping ratio of the system is
    1. 0.1026
    2. 0.3242
    3. 0.7211
    4. 0.1936

    Answer:-

  3. The eigen values of the matrix, A = are
    1. 1 and 2
    2. 1 and 2
    3. 2 and 3
    4. 2 and 4

    Answer:- 2 and 3
    |A − λI| = 0
    ⇒ | − λ| = 0
    = 0
    ⇒ (λ − 2)(λ − 3) = 0
    ⇒ λ = 2 and 3

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