Variable mass with spring

In the above system the mass of the object suspended varies with function $m(t)$ , and the spring constant of the spring is $k$ .

Let $x(t)$ be the length of the spring as time $t$ and $x_0$ as the natural length of the spring

$\Rightarrow \dfrac{d[m(t)\dot{x}(t)]}{dt}=m(t)g-kx(t)+kx_0$ Assuming $m(t)=m_0-wt,where\space w,m_0\space are\space constants$ $\Rightarrow \boxed{(m_0-wt)\ddot{x}(t)-w\dot{x}(t)+kx(t)=m_0g-wgt+kx_0}$ Now will you solve the equation?

#Mechanics

Easy Math Editor

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Comments

This is too difficult to solve analytically. Try solving it numerically and show us the result.

Krishna Karthik - 1 month, 1 week ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$