Two masses $m_{1}$ and $m_{2}$ are connected by a spring of spring constant k and are placed on a smooth horizontal surface. Initially the spring is stretched through a distance 'd' when the system is released from rest. Find the distance moved by the two masses when spring is compressed by a distance 'd'.

Open in App

Solution

Given,

Two masses $m_{1}, m_{2}$

So, Distance Stretched $= x = x_{1} + x_{2}$

Let the ratio of the distance be moved by $m_{1}$ to $m_{2}$ such that $\frac{x_{1}}{x_{2}} = \frac{m_{2}}{m_{1} + m_{2}} \Rightarrow x_{1} = \frac{m_{2} x}{m_{1} + m_{2}}$

Since $m_{1}$ agin comes to rest when it moves a distance of $2 x_{1}$

$2 x_{1} = \frac{m_{2} x}{m_{1} + m_{2}}$

Similarly,

$m_{2} = 2 x_{2} = m_{1} \frac{2 x}{m_{1} + m_{2}}$

Suggest Corrections

Similar questions

Two masses m₁and m₂ are connected by a spring of spring constant k and are placed on a smooth horizontal surface . Initially the spring is stretched through a distance d when the system is released from rest. Find the distance moved by the two masses when spring is compressed by a distance d .

Q. Two masses M1 and M2 are connected by a string constant k and are placed on a smooth horizontal surface.Initially the spring is stretched through a distance 'd' when the system is released from rest.find the distance moved by the two masses when the spring is compressed by a distance 'd'.

Q. Two masses