Simple Harmonic Motion PYQs Set 5 (PDF)

Set 5 of 13 · Questions 121-150 of 372

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Mere Teacher · Previous Year Questions JEE Main Physics · Simple Harmonic Motion · Set 5 (Q121-150)
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121. $The position of a particle in motion is given by y = C sinꞷt + D cosꞷt w.r.t. origin. Then motion of the particle is:$ (1) $SHM with amplitude C+D$ (2) $SHM with amplitude C^{2} + D^{2}$ (3) $SHM with amplitude \frac{( C + D )}{2}$ (4) $not SHM$ 122. $When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be:$ (1) $Circular$ (2) $Ellipitical$ (3) $Sinusoidal$ (4) $Straight line$ 123. $The time taken for the amplitude of vibrations of a damped oscillator to drop to 25 % of its initial value is t . The time taken for its mechanical energy to drop to 50 % of its initial mechanical energy is$ (1) $t$ (2) $\frac{t}{2}$ (3) $\frac{t}{4}$ (4) $\frac{t}{8}$ 124. $A piston is performing S.H.M. in the vertical direction with a frequency of 0.5 Hz . A block of 10 kg is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is$ (1) $1.5 m$ (2) $1 m$ (3) $0.1 m$ (4) $0.5 m$ 125. $The amplitude of a damped oscillator is known to decrease to 0.9 times its original amplitude in 5 s. Approximately, by how many times its original amplitude will decrease after another 20 s?$ (1) $0.73$ (2) $0.9$ (3) $0.59$ (4) $0.26$ 126. $Using a simple pendulum experiment g is determind by measuring its time period T . Which of the following plots represent the correct relation between the pendulum length L and time period T ?$ (1) (2) (3) (4) 127. $The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is$ (1) $100 s$ (2) $0.01 s$ (3) $10 s$ (4) $0.1 s$ 128. $The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out the time period of oscillation would$ (1) $remain unchanged$ (2) $increase towards a saturation value$ (3) $first increase and then decrease to the original value$ (4) $first decrease and then increase to the original value$ 129. $A light spring is suspended with mass m_{1} at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is T second. When a mass m_{2} is added to m_{1} and the system is made to oscillate, the period is found to be \frac{3}{2} T . The ratio of m_{1} : m_{2} is$ (1) $2 : 3$ (2) $3 : 4$ (3) $4 : 5$ (4) $5 : 6$ 130. $Average velocity of a particle executing SHM in one complete vibration is [NEET 2019]$ (1) $Aω$ (2) $Aω 22$ (3) $zero$ (4) $Aω 2$ 131. $In case of a forced vibration, the resonance wave becomes very sharp when the$ (1) $Restoring force is small$ (2) $Applied periodic force is small$ (3) $Quality factor is small$ (4) $Damping force is small$ 132. $The density of a material in SI unit of is 128 kg m^{- 3} In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is:$ (1) $40$ (2) $16$ (3) $640$ (4) $410$ 133. $If the displacement equation of a particle be represented by y = A sin PT + B cos PT, the particle executes.$ (1) $A uniform circular motion$ (2) $A uniform elliptical motion$ (3) $A S.H.M.$ (4) $A rectilinear motion$ 134. $A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force F sin ω t . If the amplitude of the particle is maximum for co = co1 and the energy of the particle is maximum for ω = ω_{2}, then$ (1) $ω_{1} \neq = ω_{0} and ω_{2} = ω_{0}$ (2) $ω_{1} = ω_{0} and ω_{2} = ω_{0}$ (3) $ω_{1} = ω_{0} and ω_{2} \neq = ω_{0}$ (4) $ω_{1} \neq = ω_{0} and ω_{2} \neq = ω_{0}$ 135. $The displacement of a damped harmonic oscillator is given by x (t) = e^{- 0.1 t} \cdot cos (10 πt + ϕ) . Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to:$ (1) $4 s$ (2) $7 s$ (3) $13 s$ (4) $27 s$ 136. $The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 \times 1 0^{-2} cosπt metres. The time at which the maximum speed first occurs is:$ (1) $0.5 s$ (2) $0.75 s$ (3) $0.125 s$ (4) $0.25 s$ 137. $A rectangular block of mass m and area of cross‐section A floats in a liquid of density p . If it is given a small vertical displacement from equilibrium it undergoes with a time period T, then$ (1) $T \propto \frac{1}{m}$ (2) $T \propto p$ (3) $T \propto \frac{1}{A}$ (4) $T \propto \frac{1}{p}$ 138. $Two simple pendulums having lengths l_{1} and l_{2} with negligible string mass undergo angular displacements θ_{1} and θ_{2}, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?$ (1) $θ_{1} l_{2} = θ_{2} l_{1}$ (2) $θ_{1} l_{1} = θ_{2} l_{2}$ (3) $θ_{1} l_{2}^{2} = θ_{2} l_{1}^{2}$ (4) $θ_{1} l_{1}^{2} = θ_{2} l_{2}^{2}$ 139. $A particle is making simple harmonic motion along the X-axis. If at a distances x_{1} and x_{2} from the mean position the velocities of the particle are v_{1} and v_{2} respectively. The time period of its oscillation is given as:$ (1) $T = 2 π \frac{x _{2}^{2} + x _{1}^{2}}{v _{1}^{2} - v _{2}^{2}}$ (2) $T = 2 π \frac{x _{2}^{2} + x _{1}^{2}}{v _{1}^{2} + v _{2}^{2}}$ (3) $T = 2 π \frac{x _{2}^{2} - x _{1}^{2}}{v _{1}^{2} + v _{2}^{2}}$ (4) $T = 2 π \frac{x _{2}^{2} - x _{1}^{2}}{v _{1}^{2} - v _{2}^{2}}$ 140. $A body executes simple harmonic motion with an amplitude A . At what displacement from the mean position is the potential energy of the body is one fourth of its total energy?$ (1) $A /4$ (2) $A /2$ (3) $3 A /4$ (4) $Some other fraction of$ 141. $A particle performs S.H.M. with amplitude 25 cm and period 3 s . The minimum time required for it to move between two points 12.5 cm on either side of the mean position is$ (1) $0.6 s$ (2) $0.5 s$ (3) $0.4 s$ (4) $0.2 s$ 142. $The potential energy of a simple harmonic oscillator of mass 2 kg at its mean position is 5 J . If its total energy is 9 J and amplitude is 1 cm, then its time period is$ (1) $\frac{π}{100} s$ (2) $\frac{π}{50} s$ (3) $\frac{π}{20} s$ (4) $\frac{π}{10} s$ 143. $A particle executes simple harmonic motion with a time period 0.6 s and amplitude 10 cm . Then the mean velocity of the particle over the time interval during which it travels a distance 5 cm starting from the equilibrium position.$ (1) $1 ms^{- 1}$ (2) $50 cm s^{- 1} .$ (3) $10 cm s^{- 1}$ (4) $1 cm s^{- 1}$ 144. $When a body is suspended from a fixed point by a spring, the angular frequency of its vertical oscillations is ꞷ_{1} . When a different spring is used, the angular frequency is ꞷ_{2} . The angular frequency of vertical oscillations when both the springs are used together in series is given by$ (1) $ω = (ω_{1}^{2} + ω_{2}^{2})^{\frac{1}{2}}$ (2) $ω = (\frac{ω _{1}^{2} + ω _{2}^{2}}{2})^{\frac{1}{2}}$ (3) $ω = (\frac{ω _{1}^{2} ω _{2}^{2}}{( ω _{1}^{2} + ω _{2}^{2} )})^{\frac{1}{2}}$ (4) $ω = (\frac{ω _{1}^{2} ω _{2}^{2}}{2 ( ω _{1}^{2} + ω _{2}^{2} )})^{\frac{1}{2}}$ 145. $A mass falls from a height ' h' and its time of fall ' t' is recorded in terms of time period T of a simple pendulum. On the surface of earth, it is found that t = 2 T . The entire set up is taken on the surface of another planet whose mass is half of earth and radius the same. Same experiment is repeated and corresponding times noted as t^{’} and T^{’} . [NEET 2019]$ (1) $t^{’} = 2 T^{’}$ (2) $t^{’} > 2 T^{’}$ (3) $t^{’} < 2 T^{’}$ (4) $t^{’} = 2 T^{’}$ 146. $The equation of a particle executing simple harmonic motion is given by x = sin π (t + \frac{1}{3}) m . At t=1s, the speed of particle will be (Given: π = 3.14)$ (1) $0 cm s^{- 1}$ (2) $157 cm s^{- 1}$ (3) $272 cm s^{- 1}$ (4) $314 cm s^{- 1}$ 147. $Time period of a simple pendulum is 2 sec. If its length is increased by 4 times, then its period becomes$ (1) $8 sec$ (2) $12 sec$ (3) $16 sec$ (4) $4 sec$ 148. $The mechanical energy of a damped oscillator becomes half of its initial energy in 4 s econds. In another t seconds its mechanical energy becomes 12.5 % of its initial mechanical energy. Then t =$ (1) $4 s$ (2) $8 s$ (3) $12 s$ (4) $16 s$ 149. $The displacement of a particle, executing simple harmonic motion with time period T, is expressed as x (t) = Asin ωt, where A is the amplitude. The maximum value of potential energy of this oscillator is found at t = T /2 β . The value of β is____.$ 150. $At a given point of time the value of displacement of a simple harmonic oscillator is given as y = A cos (30°). If amplitude is 40 cm and kinetic energy at that time is 200 J, the value offeree constant 1.0 x 1 0^{X} N m^{- 1} . The value of x is_____.$