
question_answer1) A particle moves such that its acceleration a is given by \[a=bx\], where x is the displacement from equilibrium position and b is a constant. The period of oscillation is [NCERT 1984; CPMT 1991; MP PMT 1994; MNR 1995; UPSEAT 2000]
A) \[2\pi \sqrt{b}\] done
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B) \[\frac{2\pi }{\sqrt{b}}\] done
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C) \[\frac{2\pi }{b}\] done
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D) \[2\sqrt{\frac{\pi }{b}}\] done
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question_answer2) The equation of motion of a particle is \[\frac{{{d}^{2}}y}{d{{t}^{2}}}+Ky=0\], where K is positive constant. The time period of the motion is given by [AIEEE 2005]
A) \[\frac{2\pi }{K}\] done
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B) \[2\pi K\] done
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C) \[\frac{2\pi }{\sqrt{K}}\] done
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D) \[2\pi \sqrt{K}\] done
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question_answer3) A tunnel has been dug through the centre of the earth and a ball is released in it. It will reach the other end of the tunnel after
A) 84.6 minutes done
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B) 42.3 minutes done
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C) 1 day done
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D) Will not reach the other end done
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question_answer4) The maximum speed of a particle executing S.H.M. is \[1m/s\] and its maximum acceleration is \[1.57m/se{{c}^{2}}\]. The time period of the particle will be [DPMT 2002]
A) \[\frac{1}{1.57}sec\] done
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B) 1.57 sec done
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C) 2 sec done
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D) 4 sec done
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question_answer5) The motion of a particle executing S.H.M. is given by \[x=0.01\sin 100\pi (t+.05)\], where x is in metres and time is in seconds. The time period is [CPMT 1990]
A) 0.01 sec done
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B) 0.02 sec done
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C) 0.1 sec done
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D) 0.2 sec done
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question_answer6) The kinetic energy of a particle executing S.H.M. is 16 J when it is in its mean position. If the amplitude of oscillations is 25 cm and the mass of the particle is 5.12 kg, the time period of its oscillation is [Haryana CEE 1996; AFMC 1998]
A) \[\frac{\pi }{5}\]sec done
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B) \[2\pi \]sec done
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C) \[20\pi \]sec done
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D) \[5\pi \]sec done
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question_answer7) The acceleration of a particle performing S.H.M. is \[12cm/se{{c}^{2}}\] at a distance of 3 cm from the mean position. Its time period is [MP PET 1996; MP PMT 1997]
A) 0.5 sec done
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B) 1.0 sec done
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C) 2.0 sec done
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D) 3.14 sec done
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question_answer8) To make the frequency double of an oscillator, we have to [CPMT 1999]
A) Double the mass done
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B) Half the mass done
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C) Quadruple the mass done
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D) Reduce the mass to onefourth done
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question_answer9) What is constant in S.H.M. [UPSEAT 1999]
A) Restoring force done
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B) Kinetic energy done
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C) Potential energy done
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D) Periodic time done
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question_answer10) If a simple harmonic oscillator has got a displacement of 0.02 m and acceleration equal to \[2.0m{{s}^{2}}\] at any time, the angular frequency of the oscillator is equal to [CBSE PMT 1992; RPMT 1996]
A) \[10\,rad\,{{s}^{1}}\] done
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B) \[0.1\,rad\,{{s}^{1}}\] done
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C) \[100\,rad\,{{s}^{1}}\] done
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D) \[1\,rad\,{{s}^{1}}\] done
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question_answer11) The equation of a simple harmonic motion is \[X=0.34\cos (3000t+0.74)\] where X and t are in mm and sec. The frequency of motion is [Kerala (Engg.) 2002]
A) 3000 done
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B) \[3000/2\pi \] done
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C) \[0.74/2\pi \] done
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D) \[3000/\pi \] done
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question_answer12) Mark the wrong statement [MP PMT 2003]
A) All S.H.M.?s have fixed time period done
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B) All motion having same time period are S.H.M. done
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C) In S.H.M. total energy is proportional to square of amplitude done
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D) Phase constant of S.H.M. depends upon initial conditions done
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question_answer13) A particle in SHM is described by the displacement equation \[x(t)=A\cos (\omega t+\theta ).\]If the initial (t = 0) position of the particle is 1 cm and its initial velocity is \[\pi \]cm/s, what is its amplitude? The angular frequency of the particle is \[\pi {{s}^{1}}\] [DPMT 2004]
A) 1 cm done
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B) \[\sqrt{2}\]cm done
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C) 2 cm done
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D) 2.5 cm done
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question_answer14) A particle executes SHM in a line 4 cm long. Its velocity when passing through the centre of line is 12 cm/s. The period will be [Pb. PET 2000]
A) 2.047 s done
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B) 1.047 s done
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C) 3.047 s done
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D) 0.047 s done
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question_answer15) The displacement x (in metre) of a particle in, simple harmonic motion is related to time t (in seconds) as \[x=0.01\cos \left( \pi \,t+\frac{\pi }{4} \right)\] The frequency of the motion will be [UPSEAT 2004]
A) 0.5 Hz done
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B) 1.0 Hz done
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C) \[\frac{\pi }{2}Hz\] done
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D) \[\pi \,Hz\] done
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question_answer16) A simple harmonic wave having an amplitude a and time period T is represented by the equation \[y=5\sin \pi (t+4)m.\]Then the value of amplitude (a) in (m) and time period (T) in second are [Pb. PET 2004]
A) \[a=10,\,T=2\] done
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B) \[a=5,\,T=1\] done
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C) \[a=10,T=1\] done
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D) \[a=5,\,T=2\] done
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question_answer17) A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is [CBSE PMT 2005]
A) 3 Hz done
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B) 2 Hz done
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C) 4 Hz done
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D) 1 Hz done
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question_answer18) The displacement x (in metres) of a particle performing simple harmonic motion is related to time t (in seconds) as \[x=0.05\cos \left( 4\,\pi \,t+\frac{\pi }{4} \right)\]. The frequency of the motion will be [MP PMT/PET 1998]
A) 0.5 Hz done
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B) 1.0 Hz done
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C) 1.5 Hz done
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D) 2.0 Hz done
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