Question

The total energy of a particle of mass 100gm.performing shm is 0.2J.find maximum velocity if the amplitude is 2 root 2

Answer 1

here is the answer of your question

Answer 2

Given that,

Mass of a particle, m = 100 g = 0.1 kg

Total energy of a particle, E = 0.2 J

To find,

The maximum velocity if the amplitude is $2\sqrt{2}$.

Solution,

The total energy of a particle in SHM is given by :

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

A is amplitude of particle,

$\omega=\sqrt{\dfrac{2E}{mA^2}} \\\\\omega=\sqrt{\dfrac{2\times 0.2}{0.1\times (2\sqrt 2)^2}} \\\\\omega=0.70\ rad/s$

The maximum velocity of the particle in SHM is given by :

$v=A\omega\\\\v=0.7\times 2\sqrt2\\\\v=1.97\ m/s$

Hence, the maximum velocity of the particle is 1.97 m/s.

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SHM

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