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A 1.5-kg mass attached lo spring with a force constant of 20.0 N/m oscillates on

ID: 1502702 • Letter: A

Question

A 1.5-kg mass attached lo spring with a force constant of 20.0 N/m oscillates on a horizontal, frictionless track. At = 0, the mass is released from rest at x = 10.0 cm. (That is, the spring is stretched by 10.00 cm.) Determine the frequency of the oscillations. Determine the maximum speed of the mass. Where does the maximum speed occur? Determine the maximum acceleration of the mass. Where does the maximum acceleration occur? Determine the total energy of the oscillating system. Express the displacement as a function of time.

Explanation / Answer

the force F = kx
K = F/x = 20.0/(10.0*10^-2m) = 200 N/m
the force constant K = 200 N/m
the angular frequency, = K/m = 77.547 rad
the frequency of the oscillations,
f = /2 = 77.547/2
         f = 12.34 Hz
the maximum speed Vmax = A = 7.75 m/s
the maximum Acceleration,
a max = A^2
   = 601.35 m/s^2

the total energy , E = 1/2kx^2
           E = 1/2*200*(10*10^-2)^2
         E = 1 J
the displacement ,
   y = Asint
here t = time
     y = (10.0 cm)sin77.54 t