An object of mass 6.8 kg is attached to a spring of forceconstant 1330 N/m. The

Question

An object of mass 6.8 kg is attached to a spring of forceconstant 1330 N/m. The object is set into simple harmonicmotion, with an initial velocity of vo = 4.3 m/s and aninitial displacement of
xo = 0.27m. Calculate the maximum velocity the object hasduring its motion. An object of mass 6.8 kg is attached to a spring of forceconstant 1330 N/m. The object is set into simple harmonicmotion, with an initial velocity of vo = 4.3 m/s and aninitial displacement of
xo = 0.27m. Calculate the maximum velocity the object hasduring its motion.

Explanation / Answer

The (angular) frequency of oscillation is   =(k / m) = (1330 / 6.8) = 14 / s
x = A sin ( t + )      where is the phase (the angle at t = 0) v = A cos ( t + )    we don't need the minus sign here v / x = cot ( t + ) cot = v / ( x ) = 4.3 / (.27 * 14)  =1.138 using the conditions at t = 0 tan = 1 / cot   =.880      = 41.3 deg Then using the first equation at t = 0 A = x / sin = .27 / sin 41.3 = .41 m

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