Question

A 5.00 kg mass is attached to a spring on a horizontal frictionless surface. The elastic constant of the spring is 30.8 N/m. If the mass is 28.5 cm right (+) of the equilbrium point and moving right (+) at speed 6.1 m/s, what is the initial phase of the oscillation?

Answer 1

The general solution of the spring mass system is
   
where, \phi is the initial phase.
  Now, the angular velocity is
  
So, we calculate the velocity as

So, at the initial time t =0 , taking the ratio of the position and the velocity, we get
   
  
So,
  
   
Now putting the given values, x(0) = 28.5 cm = + 0.285 m , and v(0) = + 6.1 m/s, we get