Question

Two blocks are con-
nected by a light string that
passes over two frictionless
pulleys.
The block of mass m 2 is
attached to a spring of force m1 constant k and m1 . m2.
If the system is released from rest, and the spring is initially not stretched or compressed, find an expression for the maximum dis- placement d of m2.

Answer 1

As per the given question,

the masses of the blocks are $m_1$ and $m_2$ , which is connected with the string and spring system and string is passing over the pulley, let the blocks are going x distance downwards, so the spring will elongate 2x.

Hence applying the conservation of the energy

$\Rightarrow \dfrac{k(2x)^2}{2}=m_1gx+m_2gx$

$\Rightarrow 2Kx^2=(m_1+m_2)gx$

So, x$x=\dfrac{(m_+m_2)g}{2K}$

Hence the maximum elongation in the spring will be $x=\dfrac{(m_1+m_2)g}{2K}$