The displacement of two identical particles executing SHM are represented by equations x1=4sin(10t+π6)and x2=5cosωt. For what value of ω energy of both the particles is same?

E1=E2∴12m1ω12A12=12m2ω22A22but m1=m2∴ω12×16=ω22×25∴100×16=ω2×25ω=8 units

The displacement of two identical particles executing SHM are represented by equations x1=4sin(10t+π6)and x2=5cosωt. For what value of ω energy of both the particles is same?

E1=E2∴12m1ω12A12=12m2ω22A22but m1=m2∴ω12×16=ω22×25∴100×16=ω2×25ω=8 units

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

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16 unit

6 unit

4 unit

8 unit

answer is D.

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Detailed Solution

$\begin{array}{l} E_{1} = E_{2} \\ ∴ \frac{1}{2} m_{1} ω_{1}^{2} A_{1}^{2} = \frac{1}{2} m_{2} ω_{2}^{2} A_{2}^{2} \\ {but m}_{1} = m_{2} \\ ∴ ω_{1}^{2} \times 16 = ω_{2}^{2} \times 25 \\ ∴ 100 \times 16 = ω^{2} \times 25 \\ ω = 8 units \end{array}$