The total energy of a body of mass 2 kg performing S.H.M. is 40 J. Find its speed while crossing the centre of the path.

The given data from the question can be listed as,

mass m = 2kg

Total Energy E = 40J

To find , Maximum speed i.e

$https://latex.codecogs.com/svg.image?v_{max} = ?$

Solution -

The equation for total energy can be written as ,

$https://latex.codecogs.com/svg.image?E = \frac{1}{2} m\omega ^{2}A^{2}$

$https://latex.codecogs.com/svg.image?40= \frac{1}{2} m\omega ^{2}A^{2}$

$https://latex.codecogs.com/svg.image?80= 2\omega ^{2}A^{2}$

$https://latex.codecogs.com/svg.image?40=\omega ^{2}A^{2}$

$https://latex.codecogs.com/svg.image?\sqrt{40}=\omega A$

But the maximum velocity can be written as,
$https://latex.codecogs.com/svg.image?v_{max}=\omega A$

$https://latex.codecogs.com/svg.image?v_{max}= \sqrt{40} = 6.234m/s$