Simple Harmonic Motion PYQs Set 11 (PDF)

Set 11 of 11 · Questions 301-328 of 328

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Mere Teacher · Previous Year Questions NEET Physics · Simple Harmonic Motion · Set 11 (Q301-328)
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301. $If a simple harmonic oscillator has got a displacement of 0.02 m and acceleration equal to 0.02 m / s^{2} at any time, the angular frequency of the oscillator is equal to Oscillations 123$ (1) $10 rad / s$ (2) $0.1 rad / s$ (3) $100 rad / s$ (4) $1 rad / s$ 302. $A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is:$ (1) $π^{2} m a^{2} v^{2}$ (2) $\frac{1}{4} m a^{2} v^{2}$ (3) $4 π^{2} m a^{2} v^{2}$ (4) $2 π^{2} m a^{2} v^{2}$ 303. $Amplitude of a wave is represented by A = \frac{c}{a + b - c} Then resonance will occur when$ (1) $b = - c /2$ (2) $b = 0 and a = c$ (3) $b = - a /2$ (4) $None of these$ 304. $A mass is suspended from a vertical spring which is executing. S.H.M. of frequency 5 Hz . The spring is unstretched at the highest point of oscillation. Maximum speed of the mass is [acceleration due to gravity g = 10 m / s^{2}]$ (1) $2 πm / s$ (2) $πm / s$ (3) $\frac{1}{2 π} m / s$ (4) $\frac{1}{π} m/s$ 305. $A body of mass 5 kg hangs from a spring and oscillates with a time period of 2 π seconds. If the ball is removed, the length of the spring will decrease by$ (1) $\frac{g}{k} metres$ (2) $\frac{k}{g} metres$ (3) $2 π metres$ (4) $g metres.$ 306. $Consider two SHMs along the same straight line x_{1} = A_{1} sin (ωt + φ_{1}), x_{2} = A_{2} sin (ωt + φ_{2}), where A_{1} and A_{2} are their amplitudes and φ_{1} and φ_{2} are their initial phase angle. If the two SHMs meet simultaneously and ' R' is the resultant amplitude, match column I with column II. Column-I (A). The two SHMs are in phase, A1=A2=A (B). The two SHMs are in phase, A1 \neq = A2 (C). The two SHMs are 90 out of phase, A1=A2=A (D). The two SHMs are 180^{\circ} out of phase, A1=A2 Column-II (I). R = A_{1} + A_{2} (II). R = 0 (III). R = 2 A (IV). R = 2 A$ (1) $A-III, B-I, C-IV, D-II$ (2) $A-IV, B-III, C-II, D-I$ (3) $A-I, B-III, C-II, D-IV$ (4) $A-III, B-IV, C-I, D-II$ 307. $Resonance is an example of$ (1) $Tuning fork$ (2) $Forced vibration$ (3) $Free vibration$ (4) $Damped vibration$ 308. $A simple pendulum of length 2 m is given a horizontal push through angular displacement of 60^{\circ} . If the mass of bob is 200 gram, the angular velocity of the bob will be (Take acceleration due to gravity = \frac{10 m}{s ^{2}}) (si n 30^{\circ} = co s 60^{\circ} = 0.5, co s 30^{\circ} = si n 60^{\circ} = \frac{3}{2})$ (1) $22 rad / s$ (2) $32 rad / s$ (3) $2 2.5 rad / s$ (4) $3 2.5 rad / s$ 309. $When two displacements represented by y_{1} = a sin (ω t) and y_{2} = b cos (ω t) are superimposed the motion is$ (1) $simple harmonic with amplitude a^{2} + b^{2}$ (2) $simple harmonic with amplitude \frac{( a + b )}{2}$ (3) $not a simple harmonic$ (4) $simple harmonic with amplitude \frac{a}{b}$ 310. $The displacement of a particle varies according to the relation x = 4(cosπt + sinπt). The amplitude of the particle is$ (1) $8$ (2) $- 4$ (3) $4$ (4) $42$ 311. $Which of the following statements regarding damping force of a damped oscillator is NOT correct?$ (1) $Damping force depends on the nature of the surrounding medium.$ (2) $Damping force is generally proportional to the velocity of the body making oscillations.$ (3) $Damping force acts in the direction of the velocity of the body.$ (4) $Ratio of the damping force and velocity of the body depends on the size and shape of the body.$ 312. $Two masses m and \frac{m}{2} are connected at the two ends of a massless rigid rod of length l . The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system (see figure). Because of torsional constant k, the restoring toruque is τ = kθ for angular displacement θ . If the rod is rotated by θ_{0} and released, the tension in it when it passes through its mean position will be$ (1) $\frac{3 k θ _{0}^{2}}{l}$ (2) $\frac{2 k θ _{0}^{2}}{l}$ (3) $\frac{k θ _{0}^{2}}{l}$ (4) $\frac{k θ _{0}^{2}}{2 l}$ 313. $Two blocks of masses m and M, (M > m), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then (μ = coefficient of friction between the two blocks)(A) The time period of small oscillation of the two blocks is T = 2 π \frac{( m + M )}{k} (B) The acceleration of the blocks is a = - \frac{kx}{M + m} (x = displacement of the blocks from the mean position) (C) The magnitude of the frictional force on the upper block is \frac{mμ \| x \|}{M + m} (D) The maximum amplitude of the upper block, if it does not slip, is \frac{μ ( M + m ) g}{k} (E) Maximum frictional force can be μ(M+m)g. Choose the correct answer from the options given below:$ (1) $B, C, D Only$ (2) $C, D, E Only$ (3) $A, B, D Only$ (4) $A, B, C Only$ 314. $A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency ω = \frac{π}{3} rad / s . Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of 45º as shown in the figure. Point P is at a horizontal distance of 10 cm from O. If the pebble hits the block at t = 1s, the value of v is (take g = 10 m/ s^{2})$ (1) $50 m / s$ (2) $51 m / s$ (3) $52 m / s$ (4) $53 m / s$ 315. $In case of a forced vibration, the resonance peak becomes very sharp when the$ (1) $damping force is small$ (2) $restoring force is small$ (3) $applied periodic force is small$ (4) $quality factor is small$ 316. $An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D, E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I_{0} . If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I . Then:$ (1) $I = \frac{15}{16} I_{0}$ (2) $I = \frac{3}{4} I_{0}$ (3) $I = \frac{9}{16} I_{0}$ (4) $I = \frac{I _{0}}{4}$ 317. $The total energy of particle performing SHM depend on$ (1) $k, a, m$ (2) $k, a$ (3) $k, a, x$ (4) $k, x .$ 318. $The S.H.M. of a particle is given by the equation y = 3 sin ωt + 4 cos ωt. The amplitude is:$ (1) $7$ (2) $1$ (3) $5$ (4) $12$ 319. $The S.H.M. of a particle is given by the equation y = 3 sin ω t + 4 cos ω t . The amplitude is$ (1) $7$ (2) $1$ (3) $5$ (4) $12$ 320. $The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy U (x) versus time (t) plot of the particle is correctly shown in figure:$ (1) (2) (3) (4) 321. $A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is:$ (1) $\frac{5}{π}$ (2) $\frac{5}{2 π}$ (3) $\frac{4 π}{5}$ (4) $\frac{2 π}{3}$ 322. $The amplitude of a particle due to superposition of following S.H.Ms. Along the same line is X_{1} = 2 sin 50πt ; X_{2} = 10 sin (50 πt + 37º) X_{3} = - 4 sin 50πt ; X_{4} = - 12 cos 50πt$ (1) $42$ (2) $4$ (3) $62$ (4) $none of these$ 323. $When two displacement represented by y_{1} = a sin (ꞷt) and y_{2} = b cos (ꞷt) are superimposed the motion is$ (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) $not a simple harmonic$ 324. $A simple pendulum is set into vibrations. The bob of the pendulum comes to rest after some time due to:$ (1) $Air friction$ (2) $Moment of inertia$ (3) $Weight of the bob$ (4) $Combination of all the above$ 325. $The resultant of two rectangular simple harmonic motions of the same frequency and unequal amplitudes but differing in phase by \frac{π}{2} is$ (1) $simple harmonic$ (2) $circular$ (3) $elliptical$ (4) $parabolic$ 326. $A block is in simple harmonic motion (S.H.M) on the end of the spring with position given by x = (5) cos (ωt + \frac{π}{4}) cm . If the total mechanical energy used is 100 J to achieve maximum displacement, then the potential energy at time t = 0 is$ (1) $20 J$ (2) $80 J$ (3) $75 J$ (4) $50 J$ 327. $A block of mass 100 g is connected to an elastic spring of spring constant 450 Nm^{- 1} oscillates vertically. The block-spring system is in viscous surrounding medium with a damping constant 69.3 g s^{- 1} . The time in which the amplitude of oscillations drop to half of its initial value. [take ln 2 = 0.693]$ (1) $6.93 s$ (2) $2 s$ (3) $20 s$ (4) $69.3 s$ 328. $A simple pendulum oscillates in air with time period T and amplitude A. As the time passes$ (1) $T and A both decrease$ (2) $T increases and A is constant$ (3) $T increases and A decreases$ (4) $T decreases and A is constant$