The structure shown in figure below, supports a scoreboard at a sports centre. The claxton (of...

 

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The structure shown in figure below, supports a scoreboard at a sports centre. The claxton (of total mass M) which sounds the end of playing periods includes a motor which has an unbalanced mass of 100 kg which varies sinusoidally when sounded. Using a single-degree-of-freedom model for vibrations in the vertical direction, and neglecting the mass of the truss members, determine: (i) the natural frequency and period in free vibration (9.58Hz, 0.104sec) (ii) the damping, given that a test showed 5 cycles after a 10 mm initial displacement was imposed, the amplitude was 5.30 mm (12040Ns/m) (iii) the maximum displacement when the unit's speed is 1500 rpm (0.0095mm) (iv) the speed of the machine at resonance (575rpm) (v) the displacement at resonance (1.38mm) Note: Take the following values: • For all truss members: EA = 20x10³kN; M = 5 tonnes; Ignore the stiffness and mass of member EF. 3m E L CLAXTON 3 m O 3m The structure shown in figure below, supports a scoreboard at a sports centre. The claxton (of total mass M) which sounds the end of playing periods includes a motor which has an unbalanced mass of 100 kg which varies sinusoidally when sounded. Using a single-degree-of-freedom model for vibrations in the vertical direction, and neglecting the mass of the truss members, determine: (i) the natural frequency and period in free vibration (9.58Hz, 0.104sec) (ii) the damping, given that a test showed 5 cycles after a 10 mm initial displacement was imposed, the amplitude was 5.30 mm (12040Ns/m) (iii) the maximum displacement when the unit's speed is 1500 rpm (0.0095mm) (iv) the speed of the machine at resonance (575rpm) (v) the displacement at resonance (1.38mm) Note: Take the following values: • For all truss members: EA = 20x10³kN; M = 5 tonnes; Ignore the stiffness and mass of member EF. 3m E L CLAXTON 3 m O 3m