Question

The string, the spring and the pulley shown in figure (12−E9) are light. Find the time period of the mass m.
Figure

Answer 1

The time period is $2 \pi \sqrt{\frac{m}{k}}$

Explanation:

When mass m is hung, let us consider that l be the spring’s extension Refer string1.1 below attached

In the string, let the tension be shown as $T_1$; its value is shown as

$T_1=mg=kl$

Let the string’s extension be x and the applied force is F.

Then, the tension $T_2$ has the new value and it is shown as $T_2$ = $k(x + l)$.

The difference between tensions$T_2$  and $T_1$ is the driving force.

Therefore, driving force = − $T_1$ + $T_2$ = kx

Acceleration is denoted as a, which can be obtained by using the formula, kx/m.

Time period is denoted as T, which is shown as below:

$\begin{aligned}T &=2 \pi \sqrt{\frac{\text { displacement }}{\text { Acceleration }}} \\&=2 \pi \sqrt{\frac{x}{k x / m}}=2 \pi \sqrt{\frac{m}{k}}\end{aligned}$

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Answer 2

Answer:

Explanation:

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