First slide

Simple hormonic motion

Question

A body executing SHM at a displacement ‘x’ its PE is E₁ , at a displacement ‘Y’ its PE is E₂. The P.E at a displacement (x + y) is

Easy

A

$\large \sqrt E \, = \,\sqrt {{E_1}} - \sqrt {{E_2}}$
B

$\large \sqrt E \, = \,\sqrt {{E_1}} + \sqrt {{E_2}}$
C

E = E₁ + E₂
D

E = E₁ – E₂

Solution

$\large P.E\, = \frac{1}{2}m{\omega ^2}{y^2}\, \Rightarrow \,P.E\, \propto {y^2}\, \Rightarrow \,y\, = \,k\sqrt E$
$\large x\, = \,k\sqrt {{E_1}} ;\,y\, = \,k\sqrt {{E_2}} \, \Rightarrow \,x + y\, = \,k\sqrt E$
$\large \,k\sqrt {{E_1}} + \,k\sqrt {{E_2}} \, = \,k\sqrt E \, = \,\sqrt E \, = \,\sqrt {{E_1}} \, + \,\sqrt {{E_2}}$

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