Question
The equation for displacement of two identical particles performing S.H.M. is given by $\mathrm{x}_{1}=4 \sin (20 \mathrm{t}+\mathrm{p} / 6)$ and $\mathrm{K}_{2}=10 \mathrm{sin} \omega \mathrm{t}$. For what value of $\mathrm{u}$ will both particles have same energy ?(A) 4 units(B) 8 units(C) 16 units(D) 20 unite
Step 1
Step 1: The total energy E of a particle performing simple harmonic motion is given by the formula: \[E = \frac{1}{2} m \omega^2 A^2\] where m is the mass of the particle, ω is the angular frequency, and A is the amplitude of the motion. Show more…
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If the equation for displacement of two particles executing S.H.M. is given by $\mathrm{y}_{1}=2 \sin (10 \mathrm{t}+\theta)$ and $\mathrm{y}_{2}=3 \cos 10 \mathrm{t}$ respectively, then the phase difference between the velocity of two particles will be $\ldots \ldots \ldots$ (A) $-\theta$ (B) $\theta$ (C) $\theta-(\pi / 2)$ (D) $\theta+(\pi / 2)$.
Two particles leave the origin at the same time and move along the $y$ -axis with their respective positions determined by the functions $y_{1}=\cos 2 t$ and $y_{2}=4 \sin t$ for $0<t<6$ . For how many values of $t$ do the particles have the same acceleration? (A) 0 (B) 1 (C) 2 (D) 3
The displacement of two particles executing SHM are represented by equations $$ y_{1}=2 \sin (10 t+\theta), y_{2}=3 \cos 10 t \text {. } $$ The phase difference between the velocity of these particles is (a) $\theta$ $$ \text { (b) }-\theta $$ (c) $\theta+\pi / 2$ $$ \text { (d) } \theta-\pi / 2 $$
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