A 5.0-1b bal L is fastened to the and of a tiat spring. A force ot 2.0 1b is suf

Question

A 5.0-1b bal L is fastened to the and of a tiat spring. A force ot 2.0 1b is sufticient to pu11 the bal1 6.0 in. to one stde. Plnd the toroe constant and the period ot vibzatioa. PROBLEM 362 Let the mass of the body in the diagram be 25 qm the force constant k be 400 dynes/ cm, and let the motion be started at t-0 by displacing the body 10 cm to the right of its equilibriun position and imparting to it a velocity toward the right of 40 cm/sec. Compute (a) the period T. (b) the frequency t, (c) the angular frequency u, (d) the total energy E, (e) the amplitude A, (f) the phase angle ?. (g) the naximum velocity Vnax(h) the maximum acceleration , (3) the coordinate, velocity, and acceleration at a time t/8 sec after the start of the motion

Explanation / Answer

361:

m = 5 lb = 2.27 kg

F = 2 lb = 8.90 N  

x = 8 in = 0.203 m

F = k x

k = (8.90) / 0.203 = 43.8 N/m .......Ans (Spring constant)

T = 2 pi sqrt( m / k) = 2 pi sqrt(2.27 / 43.8)

T = 1.43 sec ........Ans

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