Question

A block hangs in equilibrium from a vertical spring. When a second identical block is added, the original block sags by 5.0 cm. What is the oscillation frequency of the two- block system? - Vertical simple harmonic oscillations

Answer 1

when first block was hanging in equilibrium,

Fnet = k x0 - m g = 0

k x0 = m g .... (ii)

after second block of mass m is added,

then Fnet = k(x0 + x1 ) - (m + m)g = 0 .... (ii)

kx0 + k x1 - m g - m g = 0

m g + k x1 - m g - m g = 0

k x1 = m g

k / m = g / x1

and x1 = 5 cm = 0.05 m

k / m = (9.81) / 0.05 = 196.2

For two mass system, (2 m ) w^2 = k

w^2 = k / (2m) = (k / m) / 2 = 196.2 / 2 = 98.1

w = 9.90 rad/s