Simple Harmonic Motion PYQs Set 7 (PDF)

Set 7 of 13 · Questions 181-210 of 372

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Mere Teacher · Previous Year Questions JEE Main Physics · Simple Harmonic Motion · Set 7 (Q181-210)
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181. $The displacement of a particle executing simple harmonic motion is given by x = 2 cos (t) where t is the time in seconds then the time period of the particle is$ (1) $π second$ (2) $2 π second$ (3) $3 π second$ (4) $0.5 π second$ 182. $A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is$ (1) $\frac{5}{2 π}$ (2) $\frac{4 π}{5}$ (3) $\frac{2 π}{3}$ (4) $\frac{5}{π}$ 183. $A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m s^{- 2} at a distance of 5 m from the mean position. The time period of oscillation is$ (1) $2 πs$ (2) $πs$ (3) $2 s$ (4) $1 s$ 184. $The displacement of a particle exceuting S.H.M. is x = asin (ωt - φ) . Velocity of the particle at time t = \frac{φ}{ω} is (cos 0^{\circ} = 1)$ (1) $ωcosϕ$ (2) $aω$ (3) $ωcos2ϕ$ (4) $- aω cos2ϕ$ 185. $If a spring of stiffness 'k' is cut into two parts 'A' and 'B' of length λ_{A} : λ_{B} = 2 : 3, then the stiffness of spring 'A' is given by:$ (1) $\frac{3 k}{5}$ (2) $\frac{2 k}{5}$ (3) $k$ (4) $\frac{5 k}{2} .$ 186. $The position of a particle w.r.t. to origin varies according to the relation x = 3 sin 100 t + 8 cos^{2} 50 t . Which of the following is/are correct about this motion?$ (1) $The motion of the particle is not S.H.M.$ (2) $The amplitude of the S.H.M. of the particle is 6 units$ (3) $The amplitude of the resultant S.H.M. is 73 units$ (4) $The maximum displacement of the particle from the origin is 9 units$ 187. $When two displacements represented by y_{1} = a sin (ωt) and y_{2} = b cos (ωt) are superimposed, the motion is$ (1) $simple harmonic with amplitude \frac{a}{b}$ (2) $simple harmonic with amplitude a^{2} + b^{2}$ (3) $simple harmonic with amplitude \frac{( a + b )}{2}$ (4) $not a simple harmonic$ 188. $A pendulum oscillates simple harmonically if and only if (i) the size of the bob of pendulum is negligible in comparison with the length of the pendulum. (ii) the angular amplitude is less than 10^{\circ} .$ (1) $Both (i) and (ii) are correct.$ (2) $Both (i) and (ii) are incorrect.$ (3) $Only (i) is correct.$ (4) $Only (ii) is correct.$ 189. $Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain. Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. choose the most appropriate answer from the options given below:$ (1) $Both (A) and (R) are true and (R) is the correct explanation of (A)$ (2) $(A) is true but (R) is false$ (3) $(A) is false but (R) is true$ (4) $Both (A) and (R) are true but (R) is not the correct explanation of (A)$ 190. $A pendulum is hung from the roof of a sufficiently high building and is moving freely to and for like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/ s^{2} at a distance of 5 m from the mean position. The time period of oscillation is:$ (1) $2πs$ (2) $1 s$ (3) $2 s$ (4) $π s$ 191. $A uniform rod of length 1.8 m suspended by an end is made to undergo small oscillations. Find the length of the simple pendulum having the mass and time period equal to that of the rod.$ (1) $3.6 m$ (2) $1.2 m$ (3) $2.4 m$ (4) $4.2 m$ 192. $The equation of simple harmonic progressive wave is given by Y = asin 2 π (bt - cx) .The maximum particle velocity will be twice the wave velocity if$ (1) $c = πa$ (2) $c = \frac{1}{2 πa}$ (3) $c = \frac{1}{πa}$ (4) $c = 2 πa$ 193. $A particle is executing simple harmonic motion with an amplitude of 2 m . The difference in the magnitudes of its maximum acceleration and maximum velocity is 4. The time-period of its oscillation and its velocity when it is 1 m away from the mean position are respectively$ (1) $2 s, 23 ms^{- 1}$ (2) $\frac{7}{22} s, 43 ms^{- 1}$ (3) $\frac{22}{7} s, 23 ms^{- 1}$ (4) $\frac{44}{7} s, 43 ms^{- 1}$ 194. $A simple harmonic motion is given by y = 5 (s i n 3πt + 3 cos 3πt). What is the amplitude of motion if y is in m?$ (1) $100 cm$ (2) $5 m$ (3) $200 cm$ (4) $1000 cm$ 195. $A block resting on the horizontal surface executes S.H.M. in horizontal plane with amplitude A The frequency of oscillation for which the block just starts to slip is (μ = coefficient of friction, g = gravitational acceleration)$ (1) $\frac{1}{2 π} \frac{μg}{A}$ (2) $\frac{1}{4 π} \frac{μg}{A}$ (3) $2 π \frac{A}{μg}$ (4) $4 π \frac{A}{μg}$ 196. $The time period of mass suspended from a spring is T . If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be$ (1) $T /4$ (2) $T$ (3) $T /2$ (4) $2 T$ 197. $If two similar springs each of spring constant K_{1} are joined in series, the new spring constant and time periodwould be changed by a factor:$ (1) $\frac{1}{2}, 2$ (2) $\frac{1}{4}, 22$ (3) $\frac{1}{2}, 22$ (4) $\frac{1}{4}, 2$ 198. $Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards withan acceleration g /2, the time period of pendulum will be:$ (1) $3 T$ (2) $\frac{T}{3}$ (3) $\frac{3}{2} T$ (4) $\frac{2}{3} T$ 199. $A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to \frac{1}{1000} of the original amplitude is close to:$ (1) $50 s$ (2) $100 s$ (3) $20 s$ (4) $10 s$ 200. $The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At A/2, the kinetic energy of the block is$ (1) $37.5J$ (2) $9.75 J$ (3) $18.75 J$ (4) $12.5 J$ 201. $A particle executes simple harmonic motion according to the equation x (t) = A sin^{2} (αt) . If the time period of the SHM is 0.2 s, then the value of α (in units of rad / s) is$ (1) $2 π$ (2) $10 π$ (3) $5 π$ (4) $2.5 π$ 202. $The position vector of a particle moving in x-y plane is given by r = (A sinωt) i^+ (A cosωt) j^then motion of the particle is:$ (1) $SHM$ (2) $on a circle$ (3) $on a straight line$ (4) $with constant acceleration$ 203. $Equation of simple harmonic progressive wave is given by y = \frac{1}{a} sin ωt \pm \frac{1}{b} cos ωt, then the resultant amplitude of the wave is (cos 90^{\circ} = 0)$ (1) $\frac{a \pm b}{ab}$ (2) $\frac{a \pm b}{ab}$ (3) $\frac{a \pm b}{ab}$ (4) $\frac{a + b}{ab}$ 204. $A point mass of 400 g executes S.H.M. under a force F = - (10 Nm^{- 1}) x . If it crosses the centre of oscillation with a speed of 10 ms^{- 1}, the amplitude of motion is$ (1) $2 m$ (2) $4 m$ (3) $0.4 m$ (4) $0.5 m$ 205. $If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is \frac{x}{2} times its original time period. Then the value of x is [NEET 2024]$ (1) $3$ (2) $2$ (3) $23$ (4) $4$ 206. $A clock is designed based on the oscillations of a spring block system suspended vertically in the absence of air-resistance. Assume it shows the correct time when a spring of stiffness ' k' and block of mass ' m' are used. If the block is replaced by another block of mass 4 m, choose the correct option.$ (1) $The clock runs slow by 0.5 s for every one second$ (2) $The clock runs fast by 0.5 s for every one second$ (3) $The clock runs fast by 1 s for every one second$ (4) $The clock runs slow by 1 s for every one second$ 207. $When two mutually perpendicular simple harmonic motions of same frequency, amplitude and phase are superimposed$ (1) $the resulting motion is uniform circular motion.$ (2) $the resulting motion is a linear simple harmonic motion along a straight line inclined equally to the straight lines of motion of component ones.$ (3) $the resulting motion is an elliptical motion, symmetrical about the lines of motion of the components.$ (4) $the two S.H.M. will cancel each other.$ 208. $The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is:$ (1) $6s$ (2) $8 s$ (3) $12s$ (4) $36 s$ 209. $A particle is executing S.H.M. of periodic time ' T'. The time taken by a particle in moving from mean position to half the maximum displacement is (sin 30^{\circ} = 0.5)$ (1) $\frac{T}{2}$ (2) $\frac{T}{4}$ (3) $\frac{T}{8}$ (4) $\frac{T}{12}$ 210. $A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s . The maximum velocity of the particle is _____cm / s .$