A penguin dives from a uniform board what is hinged at the left and attached to a spring at the right . The board has length 2 m and mass 12 kg. The spring constant is 1300N/m . When the penguin dives , it leaves the board and spring oscillating with small amplitude. Assume that the board is stiff enough not to bend and with moment of inertia 1/3mL^2 , find the period of the oscillations.
hinged______________________________penguin__
2m spring <-----
Period of oscillation
2010-11-28 9:49 pm
回答 (1)
2010-11-29 1:23 am
✔ 最佳答案
Let p be angular displacement of the board during vibration.Using the formula: torque = Moment of inertia x angular acceleration
since torque = 1300.L.p
hence, 1300Lp = - (mL^2/3).a
where a is the angular acceleration of the board
i.e. a = -(1300 x 3/mL).p
a = -(1300 x 3/(12x2))p = -162.5p
The motion is therefore simple harmonic, with w^2 = 162.5 (s^-1)^2
The period of oscillation = 2.pi.square-root[1/162.5] s = 0.5 s
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