Oscillations (SHM) · JEE Main previous year questions

2018 4 questions

1. Q402018 · 16 Apr 2018 · Shift 1

   A particle executes simple harmonic motion and is located at x = a, b and c at times ${\text{t}}_0,2{\text{t}}_0$ and $3{\text{t}}_0$ respectively. The frequency of the oscillation is :

   1. A.$\frac{1}{2\pi t_0}{\cos }^{-1}\left(\frac{a+c}{2b}\right)$
   2. B.$\frac{1}{2\pi t_0}{\cos }^{-1}\left(\frac{a+b}{2c}\right)$
   3. C.$\frac{1}{2\pi t_0}{\cos }^{-1}\left(\frac{2a+3c}{b}\right)$
   4. D.$\frac{1}{2\pi t_0}{\cos }^{-1}\left(\frac{a+2b}{3c}\right)$
   Show answer

   Answer: A

2. Q522018 · 16 Apr 2018 · Shift 1

   The end correction of a resonance column is 1 cm. If the shortest length resonating with the tuning fork is 10 cm, the next resonating length should be :

   1. A.28 cm
   2. B.32 cm
   3. C.36 cm
   4. D.40 cm
   Show answer

   Answer: B

3. Q422018 · 8 Apr 2018 · Shift 1

   A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $10^{12}/sec$. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avogadro number = $6.02\times 10^{23}\mathrm{gm}\mathrm{mol}{\mathrm{e}}^{-1}$)

   1. A.$5.5N/m$
   2. B.$6.4N/m$
   3. C.$7.1N/m$
   4. D.$2.2N/m$
   Show answer

   Answer: C

4. Q582018 · 8 Apr 2018 · Shift 1

   For an RLC circuit driven with voltage of amplitude vm and frequency ${\omega }_0=\frac{1}{\sqrt{LC}}$ the current exhibits resonance. The quality factor, Q is given by :

   1. A.$\frac{CR}{{\omega }_0}$
   2. B.$\frac{{\omega }_{0}L}{R}$
   3. C.$\frac{{\omega }_{0}R}{L}$
   4. D.$\frac{R}{({\omega }_{0}C)}$
   Show answer

   Answer: B