A large, cylindrically-shaped weight is suspended from a long spring found hanging from a rafter. The weight is slender metal cylinder about two meters long that is suspended with its flat bottom about half meter above the level concrete floor. When a 1 kg mass is added, the large weight sank down an additional 3 mm. Then, after removing the mass, the larger weight is slowly made to oscillate up and down with a frequency of twelve oscillations per minute.

Question

What is the force constant of the spring?
What is the mass of the unknown weight?
If the weight is pushed down 10cm and released, how fast is it moving at its maximum speed?

Answer 1

Use this statement to determine k:
<<When a 1 kg mass is added, the large weight sank down an additional 3 mm. >>

k = m*g/X
= (1 kg)*(9.8 m/s^2))/0.003 m
m is the added mass and X is the resulting extra deflection

Use that k value and this formula to obtain M:
w = 2*pi*f = sqrt(k/M)= 2*pi*(0.2 s^-1)

Note that 12 cycles per minute was converted to frequency in Hz.
w is the angular frequency

Use this formula to determine max speed, Vmax:

Vmax = w*(amplitude)

Answer 2

Thanks for your time