The displacement of two identical particles executing SHM are represented by equations x1=4sin (10 t + (π /6)) and x2=5cos ω t For what value of ω , the energy of both the particles is the same?

Question

The displacement of two identical particles executing SHM are represented by equations x1=4sin (10 t + (π /6)) and x2=5cos ω t For what value of ω , the energy of both the particles is the same? (A) 16 unit (B) 6 unit (C) 4 unit (D) 8 unit

Tardigrade Admin · Accepted Answer

E=(1/2)mA2ω 2 i.e., E propto (A ω )2 As E1=E2 or (A1 (ω )1)2=(A2 (ω )2)2 or A1ω 1=A2ω 2 or 4× 10=5× ω or ω =8 unit

Q. The displacement of two identical particles executing SHM are represented by equations
$x_{1} = 4 s in (10 t + \frac{π}{6})$ and $x_{2} = 5 cos ω t$
For what value of $ω$ , the energy of both the particles is the same?

$16 u ni t$

$6 u ni t$

$4 u ni t$

$8 u ni t$

$E = \frac{1}{2} m A^{2} ω^{2}$ i.e., $E \propto (A ω)^{2}$
As $E_{1} = E_{2}$
or $(A_{1} (ω)_{1})^{2} = (A_{2} (ω)_{2})^{2}$
or $A_{1} ω_{1} = A_{2} ω_{2}$
or $4 \times 10 = 5 \times ω$
or $ω = 8 u ni t$

Q. The displacement of two identical particles executing SHM are represented by equations x1​=4sin(10t+6π​) and x2​=5cosωt For what value of ω , the energy of both the particles is the same?

16unit

6unit

4unit

8unit