Simple Harmonic Motion PYQs Set 4 (PDF)

Set 4 of 13 · Questions 91-120 of 372

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Physics · Simple Harmonic Motion · Set 4 (Q91-120)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
91. $The amplitudes of a damped harmonic oscillator after 2 and 4 seconds are A_{1} and A_{2} respectively. If the initial amplitude of the oscillator is A_{0}, then$ (1) $A_{1} = A_{0} A_{2}$ (2) $A_{2} = A_{0} A_{1}$ (3) $A_{0} = A_{1} A_{2}$ (4) $A_{1} = \frac{A _{0} + A _{2}}{2}$ 92. $A particle initially at the mean position is executing simple harmonic motion with an angular frequency \frac{π}{4} rad s^{- 1} . The ratio of the distances travelled by the particle in the first second and second is$ (1) $2 : 1$ (2) $1 : 1$ (3) $(1 + 3) : 1$ (4) $(1 + 2) : 1$ 93. $In a linear Simple Harmonic Motion (SHM) (A) Restoring force is directly proportional to the displacement. (B) The acceleration and displacement are opposite in direction. (C) The velocity is maximum at mean position. (D) The acceleration is minimum at extreme points. Choose the correct answer from the options given below:$ (1) $(C) and (D) only$ (2) $(A), (C) and (D) only$ (3) $(A), (B) and (C) only$ (4) $(A), (B) and (D) only$ 94. $A spring has a certain mass suspended from it and its period for vertical oscillations is ' T_{1}'. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now " T_{2} . The ratio T_{1} / T_{2} is$ (1) $2$ (2) $2$ (3) $\frac{1}{2}$ (4) $\frac{1}{2}$ 95. $Out of the following functions representing motion of a particle which represents SHM (1) y = sin ω t - cos ω t (2) y = si n^{3} ωt (3) y = 5 cos (\frac{3 π}{4} - 3 ωt) (4) y = 1 + ωt + ω^{2} t^{2}$ (1) $Only (1)$ (2) $Only (4) does not represent SHM$ (3) $Only (1) and (3)$ (4) $Only (1) and (2)$ 96. $Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500 g, Decay constant = \frac{20 g}{s} then how much time is required for the amplitude of the system to drop to half of its initial value (l n 2 = 0.693)$ (1) $34.65 s$ (2) $17.32 s$ (3) $0.034 s$ (4) $15.01 s$ 97. $A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30°. The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places (B_{Q} : B_{P}) is:$ (1) $3 :4$ (2) $4: 3$ (3) $3 :2$ (4) $2: 3$ 98. $When an oscillator completes 100 oscillations its amplitude reduced to \frac{1}{3} of initial value. What will be its amplitude, when it completes 200 oscillations:$ (1) $\frac{1}{8}$ (2) $\frac{2}{3}$ (3) $\frac{1}{6}$ (4) $\frac{1}{9}$ 99. $Which one of the following equations of motion represents simple harmonic motion? where k, k_{0}, k_{1} and a are all positive.$ (1) $Acceleration = - k (x + a)$ (2) $Acceleration = kx +a$ (3) $Acceleration = kx$ (4) $Acceleration = - k_{g} x + k_{1} x^{2}$ 100. $A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then, its time period (in seconds) is [NEET 2017]$ (1) $\frac{5}{π}$ (2) $\frac{5}{2 π}$ (3) $\frac{4 π}{5}$ (4) $\frac{2 π}{3}$ 101. $A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period T_{1} and, (ii) back and forth in a direction perpendicular to its plane, with a period T_{2} . The ratio \frac{T _{1}}{T _{2}} will be$ (1) $\frac{2}{3}$ (2) $\frac{2}{3}$ (3) $\frac{2}{3}$ (4) $\frac{3}{2}$ 102. $In a simple harmonic motion, when the displacement is one‐half the amplitude, what fraction of the total energy is kinetic?$ (1) $1/2$ (2) $3/4$ (3) $zero$ (4) $1/4.$ 103. $A force of 6.4 N stretches a vertical spring by 0.1 m . If it were to oscillate with a period of \frac{π}{4} then the mass that is to be suspended from the spring is$ (1) $\frac{π}{4} kg$ (2) $1 kg$ (3) $\frac{1}{π} kg$ (4) $10 kg$ 104. $The displacement equation of a particle is x = 3 sin 2t + 4 cos 2t, where x is in meter and t in second. The amplitude and maximum velocity will be respectively:$ (1) $5m, 10 m/s$ (2) $3m, 2 m/s$ (3) $4m, 2 m/s$ (4) $3m, 4 m/s$ 105. $A particle is performing S.H.M. starting from extreme position. Graphical representation shows that, between displacement and acceleration, there is a phase difference of$ (1) $0 rad$ (2) $\frac{π}{4} rad$ (3) $\frac{π}{2} rad$ (4) $πrad$ 106. $A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 \times 10^{- 6} J / T when a magnetic intensity of 60 \times 10^{3} A / m is applied. Its magnetic susceptibility is:$ (1) $3.3 \times 10^{- 2}$ (2) $4.3 \times 10^{- 2}$ (3) $2.3 \times 10^{- 2}$ (4) $3.3 \times 10^{- 4}$ 107. $An object of mass 0.5kg is executing simple harmonic motion. Its amplitude is 5 cm and time period (T) is 0.2s. What will be the potential energy of the object at an instant t = \frac{T}{4} s starting from mean position. Assume that the initial phase of the oscillation is zero.$ (1) $0.62J$ (2) $6.2\times 1 0^{- 3} J$ (3) $1.2 \times 1 0^{- 3} J$ (4) $3.1\times 1 0^{- 3} J$ 108. $If x, V and a denote the displacement, velocity and acceleration of a particle respectively executing simple harmonic motion of periodic time T, then which one of the following does not change with time?$ (1) $\frac{aT}{x}$ (2) $aT + 2 πV$ (3) $\frac{aT}{V}$ (4) $aT + 4 π^{2} V^{2}$ 109. $A simple pendulum of string length 30 cm performs 20 oscillations in 10 s . The length of the string required for the pendulum to perform 40 oscillations in the same time duration is____cm . [Assume that the mass of the pendulum remains same.]$ (1) $7.5$ (2) $0.75$ (3) $120$ (4) $15$ 110. $The displacement of a particle varies according to the relation x = 4 (cos πt + sin πt). The amplitude of the particle is$ (1) $4$ (2) $2$ (3) $42$ (4) $8$ 111. $For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?$ (1) $x = 0$ (2) $x = \pm A$ (3) $x = \pm \frac{A}{2}$ (4) $x = \frac{A}{2}$ 112. $A simple pendulum of length 1 m is freely suspended from the ceiling of an elevalor. The time period of small oscillations as the elevator moves up with an acceleration of 2 m / s^{2} is (use g = 10 m / s^{2})$ (1) $\frac{π}{5} s$ (2) $\frac{2}{5} πs$ (3) $\frac{π}{2} s$ (4) $\frac{π}{3} s$ 113. $A mass m_{1} connected to a horizontal spring performs S.H.M. with amplitude A . While mass m_{1} is passing through mean position another mass m_{2} is placed on it so that both the masses move together with amplitude A_{1} . The ratio of \frac{A _{1}}{A} is (m_{2} < m_{1})$ (1) $(\frac{m _{1}}{m _{1} + m _{2}})^{\frac{1}{2}}$ (2) $(\frac{m _{1} + m _{2}}{m _{1}})^{\frac{1}{2}}$ (3) $(\frac{m _{2}}{m _{1} + m _{2}})^{\frac{1}{2}}$ (4) $(\frac{m _{1} + m _{2}}{m _{2}})^{\frac{1}{2}}$ 114. $For a particle performing linear S.H.M., its average speed over one oscillation is (a = amplitude of S.H.M., n = frequency of oscillation)$ (1) $2 an$ (2) $4 an$ (3) $6 an$ (4) $8 an$ 115. $The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are:$ (1) $k g m s^{-1}$ (2) $k g m s^{-2}$ (3) $k g s^{-1}$ (4) $kgs$ 116. $For a particle executing SHM, determine the ratio of average acceleration of the particle between extreme position and equilibrium position w.r.t. the maximum acceleration.$ (1) $\frac{4}{π}$ (2) $\frac{2}{π}$ (3) $\frac{1}{π}$ (4) $\frac{1}{2 π}$ 117. $A body is executing simple harmonic motion. When the displacements from the mean position is 4 cm and 5 cm, the corresponding velocities of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is$ (1) $2 π sec$ (2) $π /2 sec$ (3) $πsec$ (4) $3 π /2 sec$ 118. $A particle of mass 250 g executes a simple harmonic motion under a periodic force F = (-25 x) N. The particle attains a maximum speed of 4m/s during its oscillation. The amplitude of the motion is _______ cm.$ 119. $The velocity of a particle executing SHM varies with displacement (x) as 4 v^{2} = 50 - x^{2} . The time period of oscillations is \frac{x}{7} s. The value of x is......... (Take π = \frac{22}{7})$ 120. $The potential energy of a particle of mass 4 kg in motion along the x-axis is given by U = 4(1 - cos 4x) J. The time period of the particle for small oscillation (sin θ ≃ θ) is (\frac{π}{K}) s . The value of K is \dots\dots$