A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant,
Question:
A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant,
its kinetic energy is $\frac{3 \mathrm{E}}{4}$ then displacement ' $y$ ' is given by :
Correct Option: , 4
Solution:
$\mathrm{E}=\frac{1}{2} \mathrm{Ka}^{2}$
$\frac{3 \mathrm{E}}{4}=\frac{1}{2} \mathrm{~K}\left(\mathrm{a}^{2}-\mathrm{y}^{2}\right)$
$\frac{3}{4} \times \frac{1}{2} \mathrm{Ka}^{2}=\frac{1}{2} \mathrm{~K}\left(\mathrm{a}^{2}-\mathrm{y}^{2}\right)$
$y^{2}=a^{2}-\frac{3 a^{2}}{4}$
$y=\frac{a}{2}$