SHM Restoring Force Equation & Phase — Practice Questions

Free NEET Physics multiple-choice questions on SHM Restoring Force Equation & Phase. Attempt each question and reveal the answer with a full explanation.

For a particle performing SHM, the graph of acceleration a versus displacement x is: A straight line with negative slope A parabola A circle A straight line with positive slope The displacement of a particle is given by x = 3 (5π t) + 4 (5π t) . The amplitude of particle motion is: 5 7 1 12 At what displacement from the mean position is the kinetic energy of a particle performing SHM equal to its potential energy? A/ 2 A/2 A/ 3 A The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where E is the total energy): E/4 E/2 2E/3 E/8 Which of the following equations represents a simple harmonic motion? d 2x dt 2 + kx = 0 d 2x dt 2 + kx 2 = 0 dx dt + kx = 0 d 2x dt 2 - kx = 0 The average potential energy of a particle executing simple harmonic motion over one complete cycle is (where E is the total energy): 1 2 E E 1 4 E Zero A particle moves in the x-y plane according to the equations x = a t and y = a ( t + /2) . The trajectory of the particle is a: Circle Ellipse Straight line Parabola A particle executing SHM passes through the mean position with a velocity v . The velocity of the particle when it has a displacement equal to half of its amplitude is: 3 v/2 v/2 v/ 2 3 v For a particle executing SHM, which of the following statements is FALSE? The total energy is zero at the mean position. The acceleration is maximum at the extreme positions. The velocity is zero at the extreme positions. The restoring force is proportional to the displacement. A particle executes SHM with period T and amplitude A . The maximum velocity of the particle is: 2 A/T A/T 2 A T 4 A/T Which of the following graphs correctly represents the variation of potential energy U with displacement x for a simple harmonic oscillator? A parabola opening upwards with vertex at (0,0) A straight line passing through origin A circle centered at origin A parabola opening downwards For a particle in SHM, which graph is a straight line passing through the origin? Acceleration vs Displacement Velocity vs Displacement Potential Energy vs Displacement Kinetic Energy vs Displacement What is the phase difference between the velocity and the acceleration of a particle executing simple harmonic motion? /2 0 3 /2 At what displacement from the mean position is the kinetic energy of a simple harmonic oscillator three times its potential energy? A/2 A/ 2 A 3 /2 A/4 A particle moves such that its acceleration a is given by a = - (x - 2) , where is a positive constant and x is the position from origin. The time period of oscillation is: 2 / 2 / 2 / Which of the following graphs correctly represents the variation of velocity v with time t for a particle starting SHM from the mean position? A cosine curve A sine curve A straight line A tangent curve Two simple harmonic motions are given by y 1 = A ( t) and y 2 = A ( t + /2) . The resultant amplitude of their superposition is: A 2 2A A A/ 2 The displacement of a particle executing simple harmonic motion is given by y = A 0 + A t + B t . Then the amplitude of its oscillation is: A 2 + B 2 A + B A 0 + A 2 + B 2 A 0 2 + (A+B) 2 If the amplitude of a simple harmonic oscillator is tripled, by what factor does the maximum kinetic energy change? 9 3 27 3 A particle executes simple harmonic motion between x = -A and x = +A . The time taken for it to go from 0 to A/2 is T 1 and to go from A/2 to A is T 2 . Then: T 1 < T 2 T 1 > T 2 T 1 = T 2 T 1 = 2T 2 The potential energy of a simple harmonic oscillator when the particle is at half its amplitude is 10 J . The total energy of the oscillator is: 40 J 20 J 80 J 10 J The displacement of a particle executing SHM is given by x = 10 (6t + /6) in SI units. The maximum acceleration of the particle is: 360 m/s 2 60 m/s 2 10 m/s 2 36 m/s 2 The displacement x (in meters) of a particle in SHM is x = 0.05 (4 t + /4) . The frequency of oscillation is: 2 Hz 4 Hz 0.5 Hz 0.25 Hz The phase difference between the displacement and acceleration of a particle in simple harmonic motion is: rad /2 rad 0 rad 3 /2 rad A particle moves in a circle with constant speed. Its motion is: Periodic but not simple harmonic Simple harmonic Neither periodic nor simple harmonic Periodic and simple harmonic The displacement of a particle is given by x = 5[ (3 t) + (3 t)] . The amplitude of the motion is: 5 2 5 10 7.5 If the maximum velocity of a particle in SHM is v 0 , then its velocity at a displacement of half its amplitude from the mean position is: 3 2 v 0 1 2 v 0 3 4 v 0 2 2 v 0 A particle executing SHM has a total energy E . When the displacement is x = A/3 (where A is amplitude), the kinetic energy is: 8 9 E 1 9 E 1 3 E 2 3 E 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 Hz 3 Hz 2 Hz 4 Hz The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is 0.707 zero 0.5 A simple pendulum performs simple harmonic motion about x=0 with an amplitude a and time period T. The speed of the pendulum at x=a/2 will be : a 3 T a 3 2T a T 3 2 a T 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 2 s s 2 s 1 s The displacement of a particle executing simple harmonic motion is given by y=A 0 + A t + B t Then the amplitude of its oscillation is given by : A + B A 0 + A 2 + B 2 A 2 + B 2 A 0 2 + (A + B) 2 The displacement of two particles in SHM are x 1 = A ( t) and x 2 = A ( t) . The phase difference between them is: /2 0 /4 Average velocity of a particle executing SHM in one complete vibration is : Zero A 2 A A 2 2 The phase difference between displacement and acceleration of a particle in a simple harmonic motion is : 3 2 rad 2 rad zero rad A body is executing simple harmonic motion with frequency ' n ', the frequency of its potential energy is 2n 3n 4n n A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is 6.28 s 3.14 s 0.628 s 0.0628 s If x = 5 ( t + 3 ) m represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are 5 cm, 2 s 5 m, 2 s 5 cm, 1 s 5 m, 1 s Two identical point masses P and Q , suspended from two separate massless springs of spring constants k 1 and k 2 , respectively, oscillate vertically. If their maximum speeds are the same, the ratio (A Q/A P) of the amplitude A Q of mass Q to the amplitude A P of mass P is k 1 k 2 k 2 k 1 k 1 k 2 k 2 k 1 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: 5 4 5 2 3 5 2 A particle executes simple harmonic motion with an amplitude A . The period of oscillation is T . What is the minimum time taken by the particle to travel from x = A to x = A/2 ? T/6 T/4 T/8 T/12 A particle starts SHM from x = A/2 and moves towards the positive extreme. Its initial phase (phase constant) in the equation x = A ( t + ) is: /6 /3 /4 5 /6 The velocity-displacement ( v-x ) graph of a particle executing SHM is: An ellipse A circle A straight line A hyperbola A particle starts SHM from the mean position. At what displacement is its kinetic energy equal to 3 times its potential energy? A/2 A/ 2 3 A/2 A/4 The displacement of a particle is given by x = A 2 t . The motion is: Simple harmonic with frequency 2 Simple harmonic with frequency Periodic but not simple harmonic Not periodic A particle executes SHM with an amplitude A . What is the average speed of the particle as it moves from the mean position to the extreme position? 2A A A 2 A A particle executes SHM such that its displacement is x = 3 ( t) + 4 ( t) . The phase constant if the equation is written in the form x = A ( t + ) is: -1 (4/3) -1 (3/4) /2 0 A particle starts SHM from its mean position. The time taken by the particle to reach its maximum speed for the first time is: T/4 T/2 T/8 T A particle is executing SHM with amplitude A and angular frequency . The average speed over one complete cycle is: 2A / A / 2 A / 2 Zero The displacement of a particle executing simple harmonic motion is given by y = A ( t) . At what displacement is the speed of the particle half of its maximum speed? 3 2 A 1 2 A 2 2 A 1 4 A The average velocity of a particle executing SHM with amplitude A and angular frequency during its motion from the mean position to the extreme position is: 2A A A 2 A A particle starts SHM from the mean position. At what time is its kinetic energy equal to its potential energy for the first time? (Let T be the time period) T/8 T/4 T/2 T/6 The displacement of a particle in SHM is x = A ( t + ) . If at t = 0 the particle is at x = -A , the phase constant is: 3 /2 /2 0 The maximum acceleration of a particle executing SHM is and maximum velocity is . The amplitude of oscillation is: 2/ / 2/ If the maximum velocity of a particle performing SHM is v m and the maximum acceleration is a m , then the amplitude of the oscillation is given by: v m 2 / a m a m 2 / v m v m / a m v m a m At t=0 , a particle executing SHM with amplitude A is at x=A/2 and moving towards the mean position. If the period is T , the time it takes to reach the mean position is: T/12 T/8 T/6 T/4 Which of the following functions of time represents periodic but NOT simple harmonic motion? t + 2 t t + t e - t ( t) The particle executing simple harmonic motion has a kinetic energy K 0 2 t . The maximum values of the potential energy and the total energy are respectively K 0/2 and K 0 K 0 and 2K 0 K 0 and K 0 0 and 2K 0 . A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m/s 2 )? 10.0 cm any value less than 12.0 cm 4.0 cm 8.0 cm A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is T/8 T/12 T/2 T/4 A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be : Mg /2k Mg /k 2 Mg /k 4 Mg /k Which one of the following equations of motion represents simple harmonic motion ? Where k, k 0 , k 1 and a are all positive Acceleration = kx Acceleration = -k 0x + k 1x 2 Acceleration = - ,k ,(x+a) Acceleration = k(x+a) The oscillation of a body on a smooth horizontal surface is represented by the equation, X = A ( t) where X = displacement at time t = frequency of oscillation Which one of the following graphs shows correctly the variation 'a' with 't' ? The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig. y - projection of the radius vector of rotating particle P is : y(t)=3 ( t 2 ) , where y in m y(t)=-3 2 t , where y in m y(t)=4 ( t 2 ) , where y in m y(t)=3 ( 3 t 2 ) , where y in m The x - t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t = 2 s is 2 8 m s -2 - 2 8 m s -2 2 16 m s -2 - 2 16 m s -2 If the frequency of an object in SHM is doubled, then its acceleration becomes: Four times Doubled Halved One-fourth In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency (t) and average amplitude A(t) of the system change with time t . Which one of the following options schematically depicts these changes correctly? Two SHMs are represented by x 1 = 5 (2 t + π/4) and x 2 = 5 2 ( 2 t + 2 t) . The ratio of their amplitudes is: 1:2 1:1 2:1 2 :1 In simple harmonic motion, the total energy E of the particle is constant. The variation of potential energy U with time t is: Periodic with frequency 2f (where f is SHM frequency) Periodic with frequency f Constant Linear The instantaneous power delivered by the restoring force to a particle of mass m executing SHM x = A ( t) is maximum when the displacement is: A / 2 0 A A/2 A particle is subjected to two perpendicular SHMs given by x = A ( t) and y = A (2 t) . The trajectory of the particle is: A parabola A circle An ellipse A straight line A particle executing SHM has a potential energy U at displacement x . The graph of U versus the velocity v is: An ellipse A circle A parabola A straight line A simple pendulum of length L and mass m has a spring of force constant k connected to the bob horizontally at its equilibrium position. If the other end of the spring is fixed, the frequency of small oscillations is: 1 2 g L + k m 1 2 g L 1 2 k m 1 2 g L - k m The equation of a simple harmonic motion is x = 0.34 (3000t + 0.74) where x and t are in mm and sec respectively. The frequency of motion is: 3000 / 2 0.74 / 2 3000 0.34 / 2 What is the phase difference between the displacement and the velocity of a particle executing SHM? /2 Zero /4