Oscillations (SHM) · JEE Main previous year questions

2004 6 questions

1. Q982004 · 24 Apr 2004 · Shift 1

   The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is $t_0$ in air. Neglecting frictional force of water and given that the density of the bob is $(4/3)\times 1000kg/{\mathrm{m}}^3$. What relationship between $t$ and $t_0$ is true

   1. A.$t=2t_0$
   2. B.$t=t_0/2$
   3. C.$t=t_0$
   4. D.$t=4t_0$
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   Answer: A

2. Q992004 · 24 Apr 2004 · Shift 1

   A particle at the end of a spring executes $S.H.M$ with a period $t_1$. While the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$ then

   1. A.$T^{-1}=t_1^{-1}+t_2^{-1}$
   2. B.$T^2=t_1^2+t_2^2$
   3. C.$T=t_1+t_2$
   4. D.$T^{-2}=t_1^{-2}+t_2^{-2}$
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   Answer: B

3. Q1002004 · 24 Apr 2004 · Shift 1

   The total energy of particle, executing simple harmonic motion is

   1. A.independent of $x$
   2. B.$\propto x^2$
   3. C.$\propto x$
   4. D.$\propto x^{1/2}$
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   Answer: A

4. Q1012004 · 24 Apr 2004 · Shift 1

   A particle of mass $m$ is attached to a spring (of spring constant $k$) and has a natural angular frequency ${\omega }_0$. An external force $F(t)$ proportional to $\cos \omega t(\omega \ne {\omega }_0)$ is applied to the oscillator. The time displacement of the oscillator will be proportional to

   1. A.$\frac{1}{m({\omega }_0^2+{\omega }^2)}$
   2. B.$\frac{1}{m({\omega }_0^2-{\omega }^2)}$
   3. C.$\frac{m}{{\omega }_0^2-{\omega }^2}$
   4. D.$\frac{m}{{\omega }_0^2+{\omega }^2}$
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   Answer: B

5. Q1222004 · 24 Apr 2004 · Shift 1

   The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $2\mathrm{s}$. The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be

   1. A.$2\sqrt{3}\mathrm{s}$
   2. B.$\frac{2}{3}\mathrm{s}$
   3. C.$2\mathrm{s}$
   4. D.$\frac{2}{\sqrt{3}}\mathrm{s}$
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   Answer: B

6. Q1432004 · 24 Apr 2004 · Shift 1

   In forced oscillation of a particle the amplitude is maximum for a frequency ${\omega }_1$ of the force while the energy is maximum for a frequency ${\omega }_2$ of the force; then

   1. A.${\omega }_1<{\omega }_2$ when damping is small and ${\omega }_1>{\omega }_2$ when damping is large
   2. B.${\omega }_1>{\omega }_2$
   3. C.${\omega }_1={\omega }_2$
   4. D.${\omega }_1<{\omega }_2$
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   Answer: C