SHM Energy & Spring-Mass Systems — Practice Questions

Free NEET Physics multiple-choice questions on SHM Energy & Spring-Mass Systems. Attempt each question and reveal the answer with a full explanation.

The kinetic energy of a simple harmonic oscillator is maximum at: The mean position The extreme positions Halfway between mean and extreme None of these 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 x 2 times its original time period. Then the value of x is: 3 2 2 3 4 For a simple pendulum, having time period T , the variation of kinetic energy (K.E.) with time ( t ) is represented by: The sum of kinetic energy and potential energy of a simple pendulum bob is 0.02 joule. The speed of the simple pendulum bob at equilibrium position is approximately: (Consider mass of the bob = 20 g) 2.0 m/s 0.2 m/s 14.1 m/s 1.41 m/s Savitha, a XI standard student, while conducting an experiment to determine the effective length of a simple pendulum L , notes down the data of time taken to complete 30 oscillations as 60 s and hence calculates the length of the simple pendulum as : (Take 2 = 9.8 , and g = 9.8 m/s 2 ) 0.75 m 1 m 1.5 m 2 m A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s . When the mass m is increased by 1 kg , the time period of oscillations becomes 5 s . The value of m in kg is: 9 16 3 4 4 3 16 9 A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of: 3 2 k 2 3 k 3k 6k Two strings A and B made of same material are stretched by same tension. The radius of A is double of B . A transverse wave travels on A with speed v A and on B with speed v B . The ratio v A/v B is: 1/2 2 1/4 4 A particle performing SHM has a total energy E . What is its kinetic energy when the displacement is half the amplitude? 3E/4 E/4 E/2 E 3 /2 The average kinetic energy of a particle executing SHM in one complete revolution is: 1 4 m 2 A 2 1 2 m 2 A 2 m 2 A 2 Zero A sonometer wire of length L vibrates in fundamental mode with frequency n . If the tension is doubled and length is halved, the new frequency will be: 2 2 n 2 n 4n n/ 2 If the tension in a string is doubled, the speed of transverse waves in it increases by a factor of: 2 2 4 1/ 2 At what displacement x from the mean position is the potential energy of a harmonic oscillator three times its kinetic energy? 3 2 A 1 2 A 1 2 A 1 3 A The work done by the restoring force in a simple harmonic oscillator as the particle moves from the mean position to the maximum displacement A is: - 1 2 k A 2 1 2 k A 2 k A 2 Zero Two strings of the same material have lengths L and 2L and radii 2r and r respectively. If they are stretched by the same force, the ratio of their fundamental frequencies will be: 1:1 1:2 2:1 4:1 A spring of force constant k is stretched by a distance x . It is further stretched by a distance y . The work done in the second stretching is: 1 2 k y(2x + y) 1 2 k y 2 1 2 k (x+y) 2 1 2 k (x 2 + y 2) The energy of a simple harmonic oscillator is E . At a displacement x = A/2 , the fraction of total energy that is kinetic is: 3/4 1/4 1/2 1/ 2 A mass m is attached to two horizontal springs of force constants k 1 and k 2 and is free to oscillate on a frictionless surface. The springs are attached to rigid walls on either side of the mass. The time period of oscillation is: 2 m k 1 + k 2 2 m(k 1 + k 2) k 1 k 2 2 m k 1 - k 2 2 m k 1 k 2 In a sonometer experiment, which of the following graphs correctly represents the relationship between the fundamental frequency n and the tension T in the wire (length remains constant)? A parabola opening towards the T -axis ( n T ) A straight line through the origin ( n T ) A rectangular hyperbola ( n 1/T ) A straight line with negative slope Two springs of force constants k 1 and k 2 are connected in series. The ratio of the potential energy stored in the springs U 1/U 2 is: k 2/k 1 k 1/k 2 (k 2/k 1) 2 k 2/k 1 A mass M is suspended from a spring of length L and force constant k . The time period is T . If the mass is removed and the spring is cut into two equal halves and the same mass M is suspended from one half, the new time period will be: T/ 2 T/2 T 2 T A block is resting on a platform which is executing vertical SHM with an amplitude A . At what minimum frequency will the block just lose contact with the platform at the highest point? 1 2 g/A g/A 2 A/g 1 2 A/g A particle executes simple harmonic motion. The ratio of its potential energy to its total energy when the displacement is one-third of its amplitude is: 1/9 1/3 2/9 1/2 For a particle executing SHM, the kinetic energy K is given by K = K 0 2 t . The maximum value of potential energy is: K 0 K 0/2 2K 0 Zero A spring of force constant k is cut into three equal parts. These three parts are then connected in parallel. The equivalent force constant of the combination is: 9k 3k k/3 k/9 The maximum velocity of a particle in SHM is v m . The velocity of the particle at a displacement equal to 3 2 times the amplitude is: v m/2 3 v m/2 v m/4 v m/ 2 For a particle in SHM, the graph of kinetic energy K against potential energy U is: A straight line with negative slope A straight line with positive slope A parabola A circle A particle executes SHM with amplitude A . What is the displacement from the mean position where the potential energy is 25 % of the total energy? A/2 A/4 A/ 2 A/ 3 A spring of force constant k is cut into two parts whose lengths are in the ratio 1:2 . The force constant of the shorter part is: 3k k/3 2k 3k/2 The average potential energy of a particle executing simple harmonic motion over one full period is: 1 4 kA 2 1 2 kA 2 kA 2 0 A spring-mass system oscillates with frequency f . If the spring is cut into two equal halves and the same mass is attached to one of the halves, the new frequency will be: 2 f 2f f/ 2 f/2 A particle executing SHM has a velocity v 1 at displacement x 1 and v 2 at displacement x 2 . Its angular frequency is: v 1 2 - v 2 2 x 2 2 - x 1 2 v 1 2 + v 2 2 x 1 2 + x 2 2 x 2 2 - x 1 2 v 1 2 - v 2 2 v 1 - v 2 x 2 - x 1 Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is: 9 10 8 11 For a particle in SHM, the kinetic energy K and potential energy U are equal when the displacement from the mean position is: A/ 2 A/2 A/ 3 3 A/2 A particle is executing SHM along a straight line. Its velocities at distances x 1 and x 2 from the mean position are v 1 and v 2 , respectively. Its time period is: 2 x 2 2 - x 1 2 v 1 2 - v 2 2 2 v 1 2 + v 2 2 x 1 2 + x 2 2 2 v 1 2 - v 2 2 x 1 2 - x 2 2 2 x 1 2 + x 2 2 v 1 2 + v 2 2 A mass M is suspended from a light spring. An additional mass m added to it displaces the spring further by distance x . The time period of oscillation of the mass (M+m) is: 2 (M+m)x mg 2 Mx mg 2 mg (M+m)x 2 (M+m)g mx A cylindrical cork of uniform density floats in a liquid of density 1 . If the cork is depressed slightly and released, it oscillates harmonically with time period T . If the same cork floats in another liquid of density 2 , then the similar oscillation has time period 2T . The value of 2/ 1 is: 4 2 1/2 1/4 Consider a spring-mass simple harmonic oscillator in one dimension. The mass of the particle is m kg and the spring constant is k Nm -1 . At a given instant, the extension of the spring is x -meter and the speed of the particle is v ms -1 . On the x-v plane, if the graph of v as a function of x is a circle, then the correct option is: k= 1 m k=m k=m 2 k= m A mass m is suspended from two springs of force constants k 1 and k 2 connected in parallel. The time period of oscillation is: 2 m k 1+k 2 2 m(k 1+k 2) k 1 k 2 2 m k 1-k 2 2 m k 1 k 2 k 1+k 2 A spring-mass system oscillates with a frequency f . If the mass is quadrupled, the new frequency of oscillation will be: f/2 2f f/4 4f A particle is executing SHM. The graph of its kinetic energy K against the displacement x is: A parabola A straight line A circle An ellipse Two springs of force constants k 1 and k 2 are connected in series. The effective force constant k is given by: k 1 k 2 k 1 + k 2 k 1 + k 2 k 1 k 2 k 1 + k 2 2 When a spring is stretched by 2 cm , its potential energy is U . If it is stretched by 10 cm , its potential energy will be: 25U 5U U/5 U/25