JEE Main & Advanced Physics Simple Harmonic Motion Question Bank

done Mock Test - Simple Harmonic Motion Total Questions - 25

• question_answer1)
  A cylindrical piston of mass M slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be
  A)
  \[T=2\pi \sqrt{\left( \frac{Mh}{PA} \right)}\]  done clear
  B)
  \[T=2\pi \sqrt{\left( \frac{Mh}{Ph} \right)}\] done clear
  C)
  \[T=2\pi \sqrt{\left( \frac{M}{PAh} \right)}\] done clear
  D)
  \[T=2\pi \sqrt{MPhA}\]   done clear
  View Solution play_arrow

• question_answer2)
  Three simple harmonic motions in the same direction having the same amplitude a and same period are superposed. If each differs in phase from the next by\[45{}^\circ \], then
  A)
  The resultant amplitude is\[\sqrt{2}a\] done clear
  B)
  The phase of the resultant motion relative to the first is \[90{}^\circ \] done clear
  C)
  The energy associated with the resulting motion is \[(3+2\sqrt{2})\] times the energy associated with any single motion done clear
  D)
  The resulting motion is not simple harmonic done clear
  View Solution play_arrow

• question_answer3)
  One end of a spring of force constant \[k\] is fixed to a vertical wall and the other to a block of mass \[m\] resting on a smooth horizontal surface. There is another wall at a distance \[{{x}_{0}}\] from the block. The spring is then compressed by \[2{{x}_{0}}\] and released. The time taken to strike the wall is
  A)
  \[\frac{1}{6}\pi \sqrt{\frac{k}{m}}\]       done clear
  B)
  \[\sqrt{\frac{k}{m}}\] done clear
  C)
  \[\frac{2\pi }{3}\sqrt{\frac{k}{m}}\]       done clear
  D)
  \[\frac{\pi }{4}\sqrt{\frac{k}{m}}\] done clear
  View Solution play_arrow

• question_answer4)
  Two particles move parallel to the \[x\]-axis about the origin with same amplitude '\[a\]' and frequency\[\omega \]. At a certain instant they are found at a distance \[a/3\] from the origin on opposite sides but their velocities are in the same direction. What is the phase difference between the two?
  A)
  \[{{\cos }^{-1}}\frac{7}{9}\]   done clear
  B)
  \[{{\cos }^{-1}}\frac{5}{9}\] done clear
  C)
  \[{{\cos }^{-1}}\frac{4}{9}\]   done clear
  D)
  \[{{\cos }^{-1}}\frac{1}{9}\] done clear
  View Solution play_arrow

• question_answer5)
  A particle perfroms SHM with a period \[T\] and amplitude \[a\]The mean velocity of the particle over the time interval during which it travels a distance all from the extreme position is
  A)
  \[a/T\]  done clear
  B)
  \[2a/T\] done clear
  C)
  \[3a/T\] done clear
  D)
  \[a/2T\] done clear
  View Solution play_arrow

• question_answer6)
  A body is executing Simple Harmonic Motion. At a displacement \[x\] its potential energy is \[{{E}_{1}}\] and at a displacement \[y\] its potential energy is \[{{E}_{2}}\] The potential energy \[E\] at displacement \[(x+y)\]is
  A)
  \[\sqrt{E}=\sqrt{{{E}_{1}}}-\sqrt{{{E}_{2}}}\] done clear
  B)
  \[\sqrt{E}=\sqrt{{{E}_{1}}}+\sqrt{{{E}_{2}}}\] done clear
  C)
  \[E={{E}_{1}}+{{E}_{2}}\]    done clear
  D)
  \[E={{E}_{1}}-{{E}_{2}}\] done clear
  View Solution play_arrow

• question_answer7)
  Two identical springs are attached to a small block\[p\]. The other ends of the springs are fixed at \[A\] and\[B\]. When \[p\]the extension of top spring is in equilibrium is 20 cm and extension p of bottom spring is 10 cm. The period of small vertical oscillations of? about its equilibrium position is (use \[g=9.8\,m/{{s}^{2}}\])
  A)
  \[\frac{2\pi }{7}\sec \]                done clear
  B)
  \[\frac{\pi }{7}\sec \] done clear
  C)
  \[\frac{2\pi }{5}\sec \]    done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer8)
  Two simple pendulum first of bob mass \[{{M}_{1}}\] and length \[{{L}_{1}}\] second of bob mass \[{{M}_{2}}\] and length\[{{L}_{2}}\]. \[{{M}_{1}}={{M}_{2}}\] and\[{{L}_{1}}=2{{L}_{2}}\]. If these vibrational energy of both is same. Then which is correct
  A)
   Amplitude of \[B\] greater than \[A\] done clear
  B)
   Amplitude of \[B\] smaller than \[A\] done clear
  C)
   Amplitudes will be same done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer9)
  A particle is executing a motion in which its displacement as a function of time is given by \[x=3\,\sin \,(5\pi t+\pi /3)+cos(5\pi t+\pi /3)\]where \[x\] is in \[m\] and \[t\] is in s. Then the motion is
  A)
   Simple harmonic with time period 0.2 s done clear
  B)
   Simple harmonic with time period 0.4 s done clear
  C)
   Simple harmonic with amplitude 3 m done clear
  D)
   Not a simple harmonic but a periodic motion done clear
  View Solution play_arrow

• question_answer10)
  A particle is subjected to two simple harmonic motions in the same direction having equal amplitude and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions, what is the phase difference between the two simple harmonic motions?
  A)
  \[\frac{2\pi }{3}\]                      done clear
  B)
  \[\frac{\pi }{3}\] done clear
  C)
  \[\frac{\pi }{\sqrt{3}}\]              done clear
  D)
  \[\frac{2\pi }{\sqrt{3}}\] done clear
  View Solution play_arrow

• question_answer11)
  One end of a spring of force constant \[k\] is fixed to a vertical wall and the other to a body of mass \[m\] resting on a smooth horizontal surface. There is another wall at a distance \[{{x}_{0}}\] from the body. The spring is then compressed by 3\[{{x}_{0}}\] and released. The time taken to strike the wall from the instant of release is (given\[{{\sin }^{-1}}(1/3)=(\pi /9))\]
  A)
  \[\frac{\pi }{6}\sqrt{\frac{m}{k}}\]         done clear
  B)
  \[\frac{2\pi }{3}\sqrt{\frac{m}{k}}\] done clear
  C)
  \[\frac{\pi }{4}\sqrt{\frac{m}{k}}\]         done clear
  D)
  \[\frac{11\pi }{9}\sqrt{\frac{m}{k}}\] done clear
  View Solution play_arrow

• question_answer12)
  A particle moves along a straight line to follow the equation\[a{{x}^{2}}+b{{v}^{2}}=k\], where\[a\], \[b\] and k are constants and \[x\] and \[v\] are x-coordinate and velocity of the particle respectively. Find the amplitude.
  A)
  \[\sqrt{\frac{k}{b}}\]                 done clear
  B)
  \[\sqrt{\frac{b}{k}}\] done clear
  C)
  \[\sqrt{\frac{a}{k}}\]                 done clear
  D)
  \[\sqrt{\frac{k}{a}}\] done clear
  View Solution play_arrow

• question_answer13)
  A particle of mass m is executing oscillations about the origin on the.\[Y\]-axis with amplitude\[A\].Its potential energy is given as\[U(x)=b{{x}^{4}}\], where \[\beta \] is a positive constant. The \[x\]-coordinate of the particle, where the potential energy is one-third of the kinetic energy, is
  A)
  \[\pm \frac{A}{2}\]                   done clear
  B)
  \[\pm \frac{A}{\sqrt{2}}\] done clear
  C)
  \[\pm \frac{A}{3}\]                   done clear
  D)
  \[\pm \frac{A}{\sqrt{3}}\] done clear
  View Solution play_arrow

• question_answer14)
  From the variation of potential energy in the direction of small oscillation of a simple pendulum, find the effective spring constant for the simple pendulum, where m is mass of the bob, \[l\] is length of the simple pendulum.
  A)
  \[\frac{mg}{l}\]             done clear
  B)
  \[\frac{mg}{2l}\] done clear
  C)
  \[\frac{2mg}{l}\]           done clear
  D)
  \[\frac{mg}{\sqrt{2}l}\] done clear
  View Solution play_arrow

• question_answer15)
  Initially cylindrical drums \[P\] and \[Q\] were placed at equal distance \[L\] from center of mass \[C\] of the rough rod \[AB\] in horizontal position. The drums were spinning in opposite directions with angular velocities. The rod is displaced by distance \[x\] towards left and released so that it performs SHM. If difference in reactions at \[Q\] and \[P\] is \[\frac{mgx}{L}\] where m is the mass of the rod, find the time period of oscillations, if m is the coefficient of friction:
  A)
  \[2\pi \sqrt{\frac{L}{g}}\]           done clear
  B)
  \[2\pi \sqrt{\frac{(L-x)}{g}}\] done clear
  C)
  \[2\pi \sqrt{\frac{(L+x)}{\mu g}}\]          done clear
  D)
  \[2\pi \sqrt{\frac{L}{\mu g}}\] done clear
  View Solution play_arrow

• question_answer16)
  The bob of a simple pendulum executes SHM in water with a period\[t\], while the period of oscillation of the bob is \[{{t}_{0}}\] in air. Neglecting the frictional force of water and given that the density of the bob is\[(4/3)\,\times 1000\,kg/{{m}^{3}}\]. What relationship between \[t\] and \[{{t}_{0}}\] is true?
  A)
  \[{{t}_{{}}}={{t}_{0}}\]         done clear
  B)
  \[{{t}_{{}}}=4{{t}_{0}}\] done clear
  C)
  \[{{t}_{{}}}=2{{t}_{0}}\]       done clear
  D)
  \[{{t}_{{}}}={{t}_{0}}/2\] done clear
  View Solution play_arrow

• question_answer17)
  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
  A)
  \[\frac{m}{{{\omega }^{2}}_{0}-{{\omega }^{2}}}\]  done clear
  B)
  \[\frac{1}{m({{\omega }^{2}}_{0}-{{\omega }^{2}})}\] done clear
  C)
  \[\frac{1}{m({{\omega }^{2}}_{0}+{{\omega }^{2}})}\]        done clear
  D)
  \[\frac{m}{{{\omega }^{2}}_{0}+{{\omega }^{2}}}\] done clear
  View Solution play_arrow

• question_answer18)
  A particle is executing SHM according to the equation\[x=A\cos \omega t\]. Average speed of the particle during the interval\[0\le t\le \frac{\pi }{6\omega }\]
  A)
  \[\frac{\sqrt{3}A\omega }{2}\]   done clear
  B)
  \[\frac{\sqrt{3}A\omega }{4}\] done clear
  C)
  \[\frac{3A\omega }{\pi }\]          done clear
  D)
  \[\frac{3A\omega }{\pi }(2-\sqrt{3})\] done clear
  View Solution play_arrow

• question_answer19)
  An object of mass \[0.2kg\] executes simple harmonic along \[X\]-axis with frequency of \[\frac{25}{\pi }Hz\]. At the position x = 0.04 m, the object has kinetic energy of 0.5 J and potential energy of 0.4 J. The amplitude of oscillation in meter is equal to
  A)
  0.05                             done clear
  B)
  0.06 done clear
  C)
   0.01                 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer20)
  A vertical mass-spring system executes simple harmonic oscillations with a period of \[2s.\,A\] quantity of this system which exhibits simple harmonic variation with a period of 1 s is
  A)
   Velocity done clear
  B)
   Potential energy done clear
  C)
   Phase difference between acceleration and dis- placement done clear
  D)
   Difference between kinetic energy and potential energy done clear
  View Solution play_arrow

• question_answer21)
  A particle is performing simple harmonic motion along x-axis with amplitude 4 cm and time period 1.2 sec. What is the minimum time (in sec) taken by the particle to move from \[X=2\] cm to \[X=+4\] cm and back again?
  View Solution play_arrow

• question_answer22)
  The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is \[K\times 10\,N/m\]. Find the value of\[K\].
  View Solution play_arrow

• question_answer23)
  Two simple pendulums of length 1 m and 16m respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed n oscillations. What is the value of\[n\]?
  View Solution play_arrow

• question_answer24)
  The displacement of a particle varies according to the relation\[X=4(cos\pi t+sin\pi t)\]. What is the amplitude of the particle?
  View Solution play_arrow

• question_answer25)
  Two SHMs are represented by the equations \[{{y}_{1}}=0.15m\]\[\left[ 100\pi t+(\pi /3) \right]\] and \[y=0.1\cos \pi t\] Tit. The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is\[-\frac{\pi }{N}\]. Find the value of\[N\].
  View Solution play_arrow