A 20 gm particle is subjected to two simple harmonic motions x 1-2 sin 10 t and x 2-4 sin10 t -3- where x 1 and x 2 are in meter - t is in secA- The displacement of the particle at t -0 will be 2 -3 mB- Maximum speed of the particle will be 20 -7 m - sC- Magnitude of maximum acceleration of the particle will be 200 -7 m - s 2D- Energy of the resultant motion will be 28 J

The correct options are A The displacement of the particle at t = 0 will be 2√(3) m B Maximum speed of the particle will be 20√(7) m/s C Magnitude of maxim ...

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Byju's Answer

Standard XII

Physics

COE in SHM

A 20 gm parti...

Question

A 20 gm particle is subjected to two simple harmonic motions $x_{1} = 2 s i n 10 t$ and $x_{2} = 4 s i n (10 t + \frac{π}{3})$ , where $x_{1}$ and $x_{2}$ are in meter & t is in sec

The displacement of the particle at t = 0 will be

2 \sqrt{3} m

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Maximum speed of the particle will be

20 \sqrt{7} m / s

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Magnitude of maximum acceleration of the particle will be

200 \sqrt{7} m / s^{2}

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Energy of the resultant motion will be 28 J

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Solution

The correct options are
A The displacement of the particle at t = 0 will be $2 \sqrt{3} m$
B Maximum speed of the particle will be $20 \sqrt{7} m / s$
C Magnitude of maximum acceleration of the particle will be $200 \sqrt{7} m / s^{2}$
D Energy of the resultant motion will be 28 J
The total displacement of the particle is
$X = X_{1} + X_{2} = 2 s i n (10 t) + 4 s i n (10 t + \frac{π}{3}) = 2 s i n 10 t + 4 s i n 10 t c o s \frac{π}{3} + 4 c o s 10 t s i n \frac{π}{3} = 4 s i n 10 t + 2 \sqrt{3} c o s 10 t = 2 \sqrt{7} s i n (10 t + ϕ) w h e r e ϕ = t a n^{- 1} (\frac{\sqrt{3}}{2})$
Hence At $t = 0; X = 2 \sqrt{7} m$
$V_{m a x} = A w = 2 \sqrt{7} \times 10 = 20 \sqrt{7} m / s a_{m a x} = A w^{2} = 2 \sqrt{7} \times 100 = 200 \sqrt{7} m / s^{2} E n e r g y = \frac{1}{2} m A^{2} w^{2} = 25 J$

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Q. A

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Q. A

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A particle is subjected to two simple harmonic motions given as $x_{1} = A_{1} s i n ω t$ and $x_{2} = A_{2} s i n (ω t + \frac{π}{3})$

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Q. A

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A 20 gm particle is subjected to two simple harmonic motions x1=2 sin 10t and x2=4 sin(10t+π3), where x1 and x2 are in meter & t is in sec

A 20 gm particle is subjected to two simple harmonic motions $x_{1} = 2 s i n 10 t$ and $x_{2} = 4 s i n (10 t + \frac{π}{3})$ , where $x_{1}$ and $x_{2}$ are in meter & t is in sec