The displacement of two identical particles executing SHM are represented by equations x 1 = 4 sin ⁡ 10 t + π 6 and x 2 = 5 cos ⁡ ω t For what value of ω , the energy of both the particles is the same?

E = 1 2 m A 2 ω 2 i.e., E ∝ 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 × 10 = 5 × ω or ω = 8 u n i t

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Physics - SHM Question with Solution | TestHub

PhysicsSHMEnergyEasy2 minPYQ_2020

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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 $x_{2} = 5 \cos ω t$

For what value of $ω$ , the energy of both the particles is the same?

Options:

Answer:

Solution:

$E = \frac{1}{2} m A^{2} ω^{2}$ 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 $ω = 8 u n i t$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:SHMSubtopic:Energy

⏱ 2mℹ️ Source: PYQ_2020

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