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1. Physics 101 Learning Object 1:
Vertical Oscillations Question
Creator: Shuanglin Cao
Question: Two blocks with the mass of m1 and m2 respectively, is attached by a light
spring (given its stiffness to be K) together (as shown in the graph below). Exert a
pressure F on m1 block. In order to bring up m2 using m1 after the pressure F is
removed, the minimum force F exerted on m2 should be ( )
A. m1g
B. 2m1g
C. (m1 +m2)g
D. 2(m1 +m2)g

2. Solution:
After the removal of pressure F, the block m1 undergoes the SHM. The balance
position of m1 is its static position on the spring (that is, without the force exerted on
its top). Assume the position to be a (as shown in the figure below), the difference of
the length of the spring without m1 block on its top and the spring with m1 on its top
(x0) is:
x0 =m1g/k
The value of the amplitude during the SHM of m1 block is equal to the decrement of
the spring with the pressure F exerted on m1 block on its top(x1).
A= x1 = F/k
Meanwhile the position of m1 block (b) is shown as follows,
Assume the spring can just lift the m2 block with the increase of its length (x2) after
the removal of the force F, thus,
Kx2 = m2*g, x2 = m2*g/k
Since x1= x0+x2
F=(m1+m2)g
The answer should be C