Question

A 0.51 kg mass at the end of a spring vibrates 10 times per second with an amplitude of 0.14 m.
Find:

1. Velocity when it passes the equilibrium point

2. The Velocity when it is 0.09 meters from equilibrium

3. The Total Energy of The System

4. The following equation describing the motion of the mass, assuming that at t = 0, x was a maximum.

______m cos[ (_______ rad/s )t ]

Answer 1

Let the displacement of the oscillating body is given by the equation

Let the velocity of the body is v_o.

We know the velocity of an oscillating body is

      

  

1)   Velocity at the equilibrial point is

  

  

  

  

  

  

2)

The velocity at when it is 0.09 meters from equilibrium

     

The velocity at when it is 0.09 meters from equilibrium 5.161187931 m/s.

3)

Let the total energy is E.

We know for an oscillating body the total energy is

      

  

The total energy is 19.73131312 J.

4) Let the equation is

Now for t=0 x=maximum or x=A the equation is