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Standard XII

Physics

Elasticity

In the figure...

Question

In the figure, the spring is compressed by $x_{0}$ and released, Two blocks $A$ and $B$ of masses $m$ and $2 m$ , respectively, are attached at the ends of the spring. Blocks are kept on a smooth horizontal surface and released. Find time Period of oscillation?

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Solution

Time period of oscillation of system is,
$T = 2 π \sqrt{\frac{μ}{k}}$ where $μ = \frac{m_{A} m_{B}}{m_{A} + m_{B}} = \frac{m (2 m)}{m + 2 m} = \frac{2 m}{3}$
$T = 2 π \sqrt{\frac{2 m}{3 k}}$

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In the figure, the spring is compressed by x0 and released, Two blocks A and B of masses m and 2m, respectively, are attached at the ends of the spring. Blocks are kept on a smooth horizontal surface and released. Find time Period of oscillation?

Time period of oscillation of system is,T=2π√μk where μ=mAmBmA+mB=m(2m)m+2m=2m3T=2π√2m3k

In the figure, the spring is compressed by $x_{0}$ and released, Two blocks $A$ and $B$ of masses $m$ and $2 m$ , respectively, are attached at the ends of the spring. Blocks are kept on a smooth horizontal surface and released. Find time Period of oscillation?

Time period of oscillation of system is,
$T = 2 π \sqrt{\frac{μ}{k}}$ where $μ = \frac{m_{A} m_{B}}{m_{A} + m_{B}} = \frac{m (2 m)}{m + 2 m} = \frac{2 m}{3}$
$T = 2 π \sqrt{\frac{2 m}{3 k}}$