A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 6.0 cm and released. If the ball makes 30 oscillations in 20 s, what are its (a) mass and (b) maximum speed?

a

b

Explanation:

From the question we are told that

    The  spring constant is  

     The  maximum extension of the spring is  

     The number of oscillation is  

      The  time taken is  

Generally the the angular speed of this oscillations is mathematically represented as

where T is the period which is mathematically represented as

substituting values

Thus  

this angular speed can also be represented mathematically as

=>  

substituting values

In SHM (simple harmonic motion )the equation for velocity is  mathematically represented as

The  velocity is maximum when  

=>  

=>    

=>  

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form