Question

a simple pendulum of mass m executes SHM with total energy E if at an instant it is at one of the extreme position then its linear momentum after a phase shift of pie/3 radian will be

Answer 1

Answer:

momentum of the pendulum at given phase is

$P = \frac{\sqrt3}{2}\sqrt{2Em}$

Explanation:

As we know that the total energy of the SHM when it is at maximum displacement position is given as E

so we have

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

now when it comes to the position of given phase

$x = A cos(\frac{\pi}{3})$

$x = \frac{A}{2}$

now velocity of the pendulum is given as

$v = \omega\sqrt{A^2 - A^2/4}$

$v = \frac{\sqrt3 A\omega}{2}$

now its momentum is given as

$P = mv$

$P = m(\frac{\sqrt3 A\omega}{2})$

$P = \frac{\sqrt3}{2}m\sqrt{\frac{2E}{m}}$

$P = \frac{\sqrt3}{2}\sqrt{2Em}$

#Learn

Topic : SHM

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