A 0.750 kg block is attached to a spring with spring constant 17.5 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 39.0 cm/scm/s . What are: a. The amplitude of the subsequent oscillations?
b. The block's speed at the point where x= 0.750 A?

a

b

The value is  

Explanation:

From the question we are told that

   The mass is  

   The spring constant is  

    The instantaneous speed is  

    The position consider is  x =  0.750A  meters from equilibrium point

Generally from the law of  energy conservation we have that

        The kinetic energy induced by the hammer  =  The energy stored in the spring

So

Here a is the amplitude of the subsequent oscillations

=>      

=>      

=>      

Generally from the law of  energy conservation we have that

The kinetic energy  by the hammer  =  The energy stored in the spring at the point considered   +   The kinetic energy at the considered point

=>          

=>          

a displacement distance is size of displ