Question

a particle is executing shm of a amplitude A at what displacement the kinetics energy three time that of potential energy​

Answer 1

Answer:

The kinetic energy and potential energy of a particle executing SHM will be equal when displacement ( amplitude = a ) is.Two particle execute SHM of the same amplitude and frequency along the same straight line. If they pass one another when going in opposite direction, each time displacement is 1/2 times their amplitude, the phase difference between them is.

Answer 2

The potential energy of a particle executing SHM is given by,

$\sf{\longrightarrow U(x)=\dfrac{1}{2}\,kx^2}$

And kinetic energy is given by,

$\sf{\longrightarrow K(x)=\dfrac{1}{2}\,k\left(A^2-x^2\right)}$

We're asked to find the displacement at which,

$\sf{\longrightarrow K(x)=3\cdot U(x)}$

$\sf{\longrightarrow\dfrac{1}{2}\,k\left(A^2-x^2\right)=\dfrac{3}{2}\,kx^2}$

$\sf{\longrightarrow A^2-x^2=3x^2}$

$\sf{\longrightarrow A^2=4x^2}$

$\sf{\longrightarrow A=\pm2x}$

$\sf{\longrightarrow\underline{\underline{x=\pm\dfrac{A}{2}}}}$