Question

A spring with spring constant 20 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 8.5 cm and released. The ball makes 28 oscillations in 18 s seconds.

A) What is its the mass of the ball?​

B) What is its maximum speed?​

Answer 1

spring constant k = 20 N/m; frequency n = 28 oscillstions/18seconds = 1.55Hz;

hence frequency of the loaded spring is n = 1/2(k/m)

1.55 = 1/2(3.14) * (20/m)

   1.55 =0.1592 (20/m)

  9.73 = (20/m)

  (9.73)² = 20/m

94.67 = 20/m

  m = 20/94.67 = 0.2112kg

B) speed of the ball V_{max ⁼} A =

here amplitude A = 8.5cm = 8.5 *10^-2 m

   = 2n = 2(3.14)(1.55) = 6.28*1.55= 9.734 rad/sec

V_max =8.5 *10^-2 * 9.734 =82.739 *10^-2 = 0.82739m/s