The length of an unstretched spring is 0.6m. The spring hangs vertically from th

Question

The length of an unstretched spring is 0.6m. The spring hangs vertically from the ceiling. Amass of 600 grams is attached to the other end of the spring which stretches the spring by 8 cm. The spring and mass are then pulled down an extra 2cm and set free to oscillate. Assume SHM.

i) With what frequency does the mass vibrate?
ii) What is the speed of the mass when it passes through the mid point of the oscillation?
iii) What is the kinetic energy of the mass at each end of the oscillation?
iv) What is the total energy stored in this oscillation?

Explanation / Answer

Length of the spring l = 0.6 m Mass of the bob m = 600 g = 0.6 Kg Elongation in the spring X = 8 cm = 0.08 m Force constant K = mg/X = (0.6*9.8)/(0.08) = 73.5 N/m Amplitude A = 2 cm = 0.02 m (1) Time period T = (2Pi)Sqrt(m/K)                       = 2*3.141*Sqrt(0.6/73.5)                       = 0.5675 s Frequency n= 1/T = 1.761 Hz (2) Velocity at mid point V = A(2*Pi*n)                                     = 0.02*2*3.141*1.761                                     = 0.2212 m/s (3) Knetic energy at extream positions K = 0 (Because velocity is 0) (4)    Total energy E = (1/2)KA^2 = 0.5*73.5*(0.02)^2                                           = 0.0147 J                          

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