SHMMedium

Question

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency $\omega(t)$ and average amplitude $A(t)$ of the system change with time t. Which one of the following options schematically depicts these changes correctly?

Options

A.
B.
C.
D.

Solution

At any point of time, time period is given by

$$T = 2\pi\sqrt{\frac{m}{k}}$$

Here $m$ is decreasing, so time period $T$ will be decreasing

Since $\omega = \frac{2\pi}{T}$

Hence as mass leaks, $\omega$ will increase

Now, at any instant

$$mg = kx_{0}$$

So, equilibrium length $x_{0} = \frac{mg}{k}$, where $m$ is decreasing

So, equilibrium length will decrease.

So, amplitude also go on decreasing.

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