Simple Harmonic Motion PYQs Set 1 (PDF)

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Mere Teacher · Previous Year Questions NEET Physics · Simple Harmonic Motion · Set 1 (Q1-30)
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1. $A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be:$ (1) $\frac{A}{2 2}$ (2) $\frac{A}{2}$ (3) $A$ (4) $\frac{A}{2}$ 2. $A cylindrical block of mass M and area of cross section A is floating in a liquid of density ρ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is____.$ (1) $π \frac{2 M}{ρAg}$ (2) $π \frac{ρA}{Mg}$ (3) $2 π \frac{ρA}{Mg}$ (4) $2 π \frac{M}{ρAg}$ 3. $A 10 kg metal block is attached to a spring of spring constant 1000 N m^{- 1} . A block is displaced from equilibrium position by 10 cm and released. The maximum acceleration of the block is$ (1) $200 m s^{- 2}$ (2) $10 m s^{- 2}$ (3) $0.1 m s^{- 2}$ (4) $100 m s^{- 2}$ 4. $The displacement of a particle is given by the relation x = 4 (cos πt + sin πt) . The amplitude of the particle is$ (1) $-4$ (2) $4$ (3) $42$ (4) $8$ 5. $Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is [NEET 2022]$ (1) $9$ (2) $10$ (3) $8$ (4) $11$ 6. $A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m / s^{2} at a distance of 5 m from the mean position. The time period of oscillation is [NEET 2018]$ (1) $2 s$ (2) $πs$ (3) $2 π s$ (4) $1 s$ 7. $For a particle executing simple harmonic motion, the kinetic energy of the particle at a distance of 4 cm from the mean position is \frac{1}{3} rd of the maximum kinetic energy. The amplitude of the motion is$ (1) $26 cm$ (2) $\frac{2}{6} cm$ (3) $2 cm$ (4) $\frac{6}{2} cm$ 8. $The average energy possessed by an oscillator at a temperature 300 K is (Boltzmann constant = 1.38 \times 10^{- 23} JK^{- 1})$ (1) $2.14 \times 10^{- 2} J$ (2) $2.07 \times 10^{- 19} J$ (3) $4.14 \times 10^{- 21} J$ (4) $None$ 9. $The ratio of kinetic energy to the potential energy of a particle executing SHM at a distance equal to half its amplitude, the distance being measured from its equilibrium position is$ (1) $4 : 1$ (2) $8 : 1$ (3) $3 : 1$ (4) $2 : 1$ 10. $The displacement of a particle along the χ ‐axis is given by χ = a si n^{2} ωt . The motion of the particle corresponds to$ (1) $simple harmonic motion of frequency ω / π$ (2) $simple harmonic motion of frequency 3 ω /2 π$ (3) $non-simple harmonic motion$ (4) $simple harmonic motion of frequency ω /2 π$ 11. $The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is$ (1) $π$ (2) $0.707 π$ (3) $zero$ (4) $0.5 π .$ 12. $A particle is executing two different simple harmonic motions, mutually perpendicular, of different amplitudes and having phase difference of \frac{π}{2} . The path of the particle will be:$ (1) $circular$ (2) $straight line$ (3) $parabolic$ (4) $elliptical$ 13. $Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be:$ (1) $A circle$ (2) $An ellipse$ (3) $A straight line$ (4) $A parabola$ 14. $The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of π results in the displacement of the particle along$ (1) $Straight line$ (2) $Circle$ (3) $Ellipse$ (4) $Figure of eight$ 15. $A sliver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1 0^{12} /sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver =108 and Avogadro number = 6.02 \times 1 0^{23} gm m o l e^{-1})$ (1) $2.2 N/m$ (2) $5.5 N/m$ (3) $6.4 N/m$ (4) $7.1 N/m$ 16. $The bob of simple pendulum of length L is released from a position of small angular displacement θ . Its linear displacement at time t is (g = acceleration due to gravity)$ (1) $Lθcos (\frac{g}{L} \cdot t)$ (2) $Lθsin (2 π \frac{g}{L} \cdot t)$ (3) $Lθcos (2 π \frac{g}{L} \cdot t)$ (4) $Lθsin (\frac{g}{L} \cdot t)$ 17. $Identify the function which represents a periodic motion. [NEET 2020]$ (1) $e^{ωt}$ (2) $log_{e} (ωt)$ (3) $sin ωt + cos ωt$ (4) $e^{- ωt}$ 18. $Two springs of spring constants k_{1} and k_{2} are joined in series. The effective spring constant of the combination is given by$ (1) $k_{1} k_{2}$ (2) $k_{1} + k_{2} /2$ (3) $k_{1} + k_{2}$ (4) $k1k2/ k_{1} + k_{2}$ 19. $Two bodies A and B of equal mass are suspended from two massless springs of spring constant k_{1} and k_{2}, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is$ (1) $\frac{k _{1}}{k _{2}}$ (2) $\frac{k _{1}}{k _{2}}$ (3) $\frac{k _{2}}{k _{1}}$ (4) $\frac{k _{2}}{k _{1}}$ 20. $In a simple pendulum experiment for determination of acceleration due to gravity (g) time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s . The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm The percentage error in the determination of g is close to:$ (1) $0.7 %$ (2) $0.2 %$ (3) $3.5 %$ (4) $6.8 %$ 21. $The displacement of a particle executing SHM is given by x = 3 sin (2 πt + \frac{π}{4}) where ' x' is in metres and ' t' is in seconds. The amplitude and maximum speed of the particle is$ (1) $3 m, 6 πm s^{- 1}$ (2) $3 m, 2 πm s^{- 1}$ (3) $3 m, 8 πm s^{- 1}$ (4) $3 m, 4 πm s^{- 1}$ 22. $The equation of motion of a particle executing simple harmonic motion is given by x = 3 sin (6 t + \frac{π}{6}), where x is in metres and t is in seconds. The ratio of the potential and kinetic energies of the particle at time t = 0 is$ (1) $1 : 1$ (2) $1 : 4$ (3) $1 : 2$ (4) $1 : 3$ 23. $A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of f is:$ (1) $\frac{1}{2}$ (2) $2$ (3) $1$ (4) $\frac{1}{2}$ 24. $Two particles are executing simple harmonic motion of the same amplitude A and frequency ꞷ along the x-axis. Their mean position is separated by distance X_{0} (X_{0} > A). If the maximum separation between them is (X_{0} + A), the phase difference between their motion is:$ (1) $\frac{π}{2}$ (2) $\frac{π}{3}$ (3) $\frac{π}{4}$ (4) $\frac{π}{6}$ 25. $A block of mass ' M' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that the mass is separated from the piston, is (acceleration due to gravity, g = 10 ms^{- 2}, π^{2} = 10)$ (1) $0.25 m$ (2) $0.5 m$ (3) $1 m$ (4) $\infty$ 26. $For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)$ (1) (2) (3) (4) 27. $Two springs of force constants k_{1} and k_{2} are loaded with weights w_{1} and w_{2} respectively. Assume that, length of each string is increased by same amount. If k_{1} = 2 k_{2}, then the ratio w_{2} / w_{1} is$ (1) $1$ (2) $0.5$ (3) $0.25$ (4) $4$ 28. $Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet. Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet. choose the correct answer from the options given below:$ (1) $(A) is false but (R) is true$ (2) $(A) is true but (R) is false$ (3) $Both (A) and (R) are true and (R) is the correct explanation of (A)$ (4) $Both (A) and (R) are true but (R) is NOT the correct explanation of (A)$ 29. $Two particles A and B of equal masses are suspended from two massless springs of spring constants K_{1} and K_{2} respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is$ (1) $\frac{K _{2}}{K _{1}}$ (2) $\frac{K _{1}}{K _{2}}$ (3) $\frac{K _{1}}{K _{2}}$ (4) $\frac{K _{2}}{K _{1}}$ 30. $The displacement of a particle executing simple harmonic motion is given by y = A_{0} + Asi n ωt + Bco s ωt Then, the amplitude of its oscillation is given by [NEET 2019]$ (1) $A^{2} + B^{2}$ (2) $A02+(A + B)2$ (3) $A + B$ (4) $A_{0} + A^{2} + B^{2}$