Problem 2: A body of mass 0.025 kg attached to a spring is displaced through 0.1 m to right of the mean position, if spring constant is of the spring is 0.4 N/m and its velocity at the end of this displacement be 0.4 m/s. Calculate

(i) Time period                  (ii) Frequency              (iii) Angular speed w                       (iv) Total energy (v) The amplitude            (vi) Maximum velocity  

(vii) The maximum acceleration

Answer

Given Mass, m = 0.025 kg spring constant, k = 0.4 N/m displacement, x = 0.1 velocity, v = 0.4 m/s

(i) Formula

Put values,

(ii) Formula

Put value of T from the above equation

(iii) Formula

Put the value of f from the above equation

(iv) Formula

Put values

(v) We know that the P.E energy at the extreme point is equal to the total energy of the system. Therefore,

(vi) When K.E is maximum, velocity is also maximum

(vii) Since

Put values