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**Hint**We have a simple body executing the simple harmonic motion and by applying the formula of energy which is$\dfrac{1}{2}m{\omega ^2}{A^2}$, we will be able to find the total required energy for the system. And while solving this we have to keep in mind to change the units of the needed entities.

**Formula used**

The total energy of the system,

$E = \dfrac{1}{2}m{\omega ^2}{A^2}$

Here,

$E$, will be the energy

$m$, will be the mass

$\omega $, will be the angular velocity

$A$, will be the area

Also, the formula for the angular velocity will be,

$\omega = \dfrac{{2\pi }}{T}$

Here,

$T$, will be the time period.

**Complete Step By Step Solution**So we have to find the total energy, for this, we will use the formula for the total energy mentioned in the formula.

$E = \dfrac{1}{2}m{\omega ^2}{A^2}$

So the above equation can also be written as,

\[E = \dfrac{1}{2}m{\left( {\dfrac{{2\pi }}{T}} \right)^2}{A^2}\]

Now on substituting the values, we get

Also while putting the values we had changed the units,

The equation will be like,

$ \Rightarrow \dfrac{{2{\pi ^2}\left( {400 \times {{10}^{ - 3}}kg} \right){{\left( {20 \times {{10}^{ - 2}}m} \right)}^2}}}{{0.20s}}$

Now on simplifying the above equations, we get

$ \Rightarrow 1.577J$

**Therefore, $1.577J$ energy is required for the system.**

**Note**Mechanical energy, the aggregate of the active energy, or energy of movement, and the possible energy, or energy put away in a framework because of the situation of its parts. Mechanical energy is consistent in a framework that has just gravitational powers or in a generally admired framework—that is, one lacking dissipative powers, for example, erosion and air obstruction, or one in which such powers can be sensibly ignored. In this manner, a swinging pendulum has its most prominent dynamic energy and least possible energy in the vertical situation, in which its speed is most noteworthy and its stature least; it has its most un-motor energy and most prominent likely energy at the limits of its swing, in which its speed is zero and its tallness is most noteworthy.

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