Question

The amplitude of a particle executing SHM is made three fourth keeping its time period constant, Its total energy will be :-

• A. $\frac{E}{2}$
• B. $\frac{E}{2}E$
• C. $\frac{9}{16}E$
• D. None of these

Answer 1

The correct option is A $\frac{E}{2}$

$E=\frac{1}{2}m{\omega }^2{a}^2\Rightarrow \frac{E^{\prime }}{E}=\frac{a^{\prime 2}}{a^2}$

$\Rightarrow \frac{E^{\prime }}{E}=\frac{{\left(\frac{3}{4}a\right)}^2}{a^2}$ $(\because a^{\prime }=\frac{3}{4}a)$

$\Rightarrow E^{\prime }=\frac{9}{16}E$