Simple Harmonic Motion PYQs Set 8 (PDF)

Set 8 of 13 · Questions 211-240 of 372

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Mere Teacher · Previous Year Questions JEE Main Physics · Simple Harmonic Motion · Set 8 (Q211-240)
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211. $A S.H.M. is represented by x = 52 (sin 2 πt + cos 2 πt) . The amplitude of the S.H.M. is$ (1) $10 cm$ (2) $20 cm$ (3) $52 cm$ (4) $50 cm$ 212. $The equation of motion of a particle performing linear S.H.M is x = 5 sin (4 t - \frac{π}{6}), where ' x' is its displacement in cm . The velocity of the particle when its displacement is 3 cm, is$ (1) $10 cm / s$ (2) $16 cm / s$ (3) $6 cm / s$ (4) $8 cm / s$ 213. $A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be$ (1) $1:1$ (2) $1 : 3$ (3) $2 : 1$ (4) $1 : 4$ 214. $A particle performs linear S.H.M. At a particular instant, velocity of the particle is u and acceleration is α while at another instant velocity is v and acceleration is β (0 < α < β) . The distance between the two positions is$ (1) $\frac{u ^{2} - v ^{2}}{α + β}$ (2) $\frac{u ^{2} + v ^{2}}{α + β}$ (3) $\frac{u ^{2} - v ^{2}}{α - β}$ (4) $\frac{u ^{2} + v ^{2}}{α - β}$ 215. $If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?$ (1) $\frac{a T}{x}$ (2) $aT + 2πv$ (3) $\frac{a T}{v}$ (4) $a2T2 + 4π2v2$ 216. $The displacement of a particle along the x axis is given by x = a s i n^{2} ꞷt. The motion of the particle corresponds to$ (1) $simple harmonic motion of frequency ꞷ/π$ (2) $simple harmonic motion of frequency 3ꞷ/2π$ (3) $non simple harmonic motion$ (4) $simple harmonic motion of frequency ꞷ/2π$ 217. $A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density \frac{1}{4} times that of the bob and the length of the thread is increased by 1/ 3^{r d} of the original length, then the time period of the simple harmonic oscillations will be:-$ (1) $T$ (2) $\frac{3}{2} T$ (3) $\frac{3}{4} T$ (4) $\frac{4}{3} T$ 218. $When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by y (t) = y_{0} sin^{2} ωt, where y^{’} is measured from the lower end of unstretched spring. Then ω is$ (1) $\frac{2 g}{y _{0}}$ (2) $\frac{1}{2} \frac{g}{y _{0}}$ (3) $\frac{g}{2 y _{0}}$ (4) $\frac{g}{y _{0}}$ 219. $A mass is suspended from a spring having spring constant ' K' is displaced vertically and released, oscillates with period ' T'. The weight of the mass suspended is (g = gravitational acceleration)$ (1) $\frac{KTg}{4 π ^{2}}$ (2) $\frac{K T ^{2} g}{4 π ^{2}}$ (3) $\frac{KTg}{2 π ^{2}}$ (4) $\frac{K T ^{2} g}{2 π ^{2}}$ 220. $The resultant of two rectangular simple harmonic motions of the same frequency and unequal amplitudes but differing in phase by π/2 is:$ (1) $Simple harmonic$ (2) $Circular$ (3) $Elliptical$ (4) $Parabolic$ 221. $A clock pendulum having coefficient of linear expansion α = 9 \times 10^{- 7} /^{\circ} C has a period of 0.5 s at 20^{\circ} C . If the clock is used in a climate where the temperature is 30^{\circ} C, how much time does the clock lose in each oscillation? (g = constant)$ (1) $25\times 1 0^{- 7} s$ (2) $5 \times 10^{- 7} s$ (3) $1.125 \times 10^{- 6} s$ (4) $2.25 \times 10^{- 6} s$ 222. $Two masses M_{A} and M_{B} are hung from two smngs of length l_{A} and l_{B} respectively. They are executing SHM with frequency relation f_{A} = 2 f_{B}, then relation$ (1) $l_{A} = \frac{l _{B}}{4}, does not depend on mass$ (2) $l_{A} = 4 l_{B}, does not depend on mass$ (3) $l_{A} = 2 l_{B} and M_{A} = 2 M_{B}$ (4) $l_{A} = \frac{l _{B}}{2} and M_{A} = \frac{M _{B}}{2} .$ 223. $The function of time representing a simple harmonic motion with a period of \frac{π}{ω} is:$ (1) $sin (ωt) + cos (ωt)$ (2) $cos (ωt) + cos (2 ωt) + cos (3 ωt)$ (3) $sin^{2} (ωt)$ (4) $3 cos (\frac{π}{4} - 2 ωt)$ 224. $Abode of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s . When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s . The value of m in kg is$ (1) $\frac{3}{4}$ (2) $\frac{4}{3}$ (3) $\frac{16}{9}$ (4) $\frac{9}{16}$ 225. $A spring is stretched by 0.40 m when a mass of 0.6 kg is suspended from it. The period of oscillations of the spring loaded by 255 g and put to oscillations is close to (g = 10 ms^{- 2})$ (1) $11 s$ (2) $48.6 s$ (3) $0.82 s$ (4) $4.86 s$ 226. $A simple pendulum is oscillating with amplitude ' A' and angular frequency ' ω'. At displacement ' x' from mean position, the ratio of kinetic energy to potential energy is$ (1) $\frac{x ^{2}}{A ^{2} - x ^{2}}$ (2) $\frac{x ^{2} - A ^{2}}{x ^{2}}$ (3) $\frac{A ^{2} - x ^{2}}{x ^{2}}$ (4) $\frac{A - x}{x}$ 227. $Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulums is$ (1) $\frac{49}{81}$ (2) $\frac{64}{81}$ (3) $\frac{8}{9}$ (4) $\frac{7}{9}$ 228. $If x = 5 sin (πt + \frac{π}{3}) m represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are [NEET 2024]$ (1) $5 cm, 2 s$ (2) $5 m, 2 s$ (3) $5 cm, 1 s$ (4) $5 m, 1 s$ 229. $A particle executes SHM with amplitude 0.2 m and time period 24 s . The time required for it to move from the mean position to a point 0.1 m from the mean position is$ (1) $2 s$ (2) $3 s$ (3) $8 s$ (4) $12 s$ 230. $A loop of radius R and mass m is placed in a uniform magnetic field B with its plane perpendicular to the field. Current I is flowing in it. Now loop is slightly rotated about its diameter and released. Find time period of oscillation.$ (1) $2 \frac{πm}{lB}$ (2) $\frac{2 πm}{lB}$ (3) $2 \frac{m}{πIB}$ (4) $\frac{m}{πIB}$ 231. $A linear harmonic oscillator of force constant 2 \times 1 0^{6} N / m and amplitude 0.01 m has a total mechanical energy of160 J. Its$ (1) $P.E. is 160 J$ (2) $P.E. is zero$ (3) $P.E. is 100 J$ (4) $P.E. is 120 J.$ 232. $A particle is subjected to two simple harmonic motions along x and y directions according to x = 3 sin 100 πt; y = 4 sin 100 πt Choose the correct option.$ (1) $Motion of particle will be elliptical, traversing in clockwise direction$ (2) $Particle will move on a straight line of slope 4/3$ (3) $Particle will have simple harmonic motion along x -axis with amplitude 5 units.$ (4) $Particle will transverse a hyperbola.$ 233. $A particle is vibrating in S.H.M. with an amplitude of 4 cm . At what displacement from the equilibrium position is its energy half potential and half kinetic?$ (1) $1 cm$ (2) $2 cm$ (3) $2 cm$ (4) $22 cm$ 234. $A particle undergoing simple harmonic motion has time dependent displacement given by x (t) = A sin \frac{πt}{90} . The ratio of kinetic to potential energy of this particle at t = 210 s will be$ (1) $1/9$ (2) $1$ (3) $1/3$ (4) $1/2$ 235. $Two simple pendulums A and B are made to oscillate simultaneously and it is found that A completes 10 oscillations in 20 s and B completes 8 oscillations in 10 s . The ratio of the lengths of A and B is$ (1) $5/4$ (2) $8/5$ (3) $25/64$ (4) $64/25$ 236. $A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm / s . The frequency of its oscillation is$ (1) $4 Hz$ (2) $3 Hz$ (3) $2 Hz$ (4) $1 Hz.$ 237. $A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude 12 cm . After 2 minutes the amplitude decreasesto 6 cm . Determine the value of the dampingconstant for this motion. (take In 2 = 0.693)$ (1) $0.69 \times 10^{2} kg s^{- 1}$ (2) $3.3 \times 10^{2} kg s^{- 1}$ (3) $1.16 \times 10^{- 2} kg s^{- 1}$ (4) $5.7 \times 10^{- 3} kg s^{- 1}$ 238. $Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the 3 times of amplitude of individual motions. The phase difference between the two motions is_____(degree)$ 239. $Two simple harmonic motion, are represented by the equations y_{1} = 10 sin (3 πt + \frac{π}{3}), y_{2} = 5 (sin 3 πt + 3 cos 3 πt) Ratio of amplitude of y_{1} to y_{2} = x : 1 . The value of x is .......$ 240. $The displacement of a particle executing SHM is given by x = 10 sin (wt + \frac{π}{3}) m . The time period of motion is 3.14 s . The velocity of the particle at t = 0 is _____m / s .$