Question

The displacement of two identical particles executing SHM are represented by equations
$x_{1}=4sin \left(10 t + \frac{\pi }{6}\right)$ and $x_{2}=5cos \omega t$
For what value of $\omega $ , the energy of both the particles is the same?

• A. $16 \, unit$
• B. $6 \, unit$
• C. $4 \, unit$
• D. $8 \, unit$

Answer 1

Answer: (D)

$E=\frac{1}{2}mA^{2}\omega ^{2}$ i.e., $E \propto \left(A \omega \right)^{2}$
As $E_{1}=E_{2}$
or $\left(A_{1} \left(\omega \right)_{1}\right)^{2}=\left(A_{2} \left(\omega \right)_{2}\right)^{2}$
or $A_{1}\omega _{1}=A_{2}\omega _{2}$
or $4\times 10=5\times \omega $
or $\omega =8 \, unit$