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1 Equations. A body executing simple harmonic motion has maximum acceleration ) At the mean positions ) At the two extreme position 3) At any position 4) he question is irrelevant. A particle moves on the x-axis according to the equation x = A + B sin ωt. he motion is simple harmonic with amplitude ) A ) B 3) A + B 4) A + B 3. If the maximum acceleration of a S.H.M. is a and the maximum velocity is b, then amplitude of vibration is given by ) b a ) a b 3) 4. For a particle executing S.H.M, which of the following statements is not correct? ) he total energy of a particle always remains the same ) he restoring force is always directed towards a fixed point 3) he restoring force is maximum at the extreme positions 4) he acceleration of the particle is maximum at the equilibrium position 5. Choose the correct statement. a) Any motion that repeats itself in equal intervals of time along the same path is called periodic motion. b) he displacement of a particle in periodic motion can always be expressed in terms of sine and cosine functions of time. b a 4) a b

2 c) A body in periodic motion moves back and forth over the same path is called oscillatory or vibrating motion. d) Simple harmonic motion is a particular case of periodic motion. ) Only a, b, d are true ) Only b, c, d are true 3) Only a, c, d are true 4) All are true 6. In a periodic motion when a body moves to and fro about a fixed mean position its acceleration. ) Proportional to displacement of body from mean position and is always directed towards the mean position. ) Inversely proportional to displacement of body from mean position and is always directed away from mean position. 3) Proportional to displacement of body from mean position and is always directed away from mean position 4) May be proportional to displacement but unspecified direction. 7. In S.H.M. ) he acceleration and displacement of a body are proportional to each other and opposite in direction. ) he accelerations and displacement of body are proportional to each other and same in direction. 3) he acceleration and displacement of body are inversely proportional to each other and opposite in direction. 4) he acceleration and displacement are inversely proportional to each other and same in direction.

3 8. he uniform circular motion in general can be described as a combination of two simple harmonic motions. ) Acting perpendicular to each other ) Acting parallel to each other 3) Acting anti parallel to each other 4) Acting inclines to each other with less than Statement (a): he velocity of simple harmonic oscillator is maximum at mean position Statement (b): At extreme position the acceleration of simple harmonic oscillator is maximum. Statement (c): he velocity of simple harmonic oscillator is minimum at extreme position ) a, b are true ) Only a is true 3) b, c are true 4) All are true 0. For a simple harmonic oscillator the frequency of oscillation is independent of ) ime period ) Acceleration 3) Angular velocity 4) Amplitude. he phase difference between velocity and acceleration of simple harmonic oscillator. ) ) 3) 4 4) 3. he phase difference between acceleration and displacement of simple harmonic oscillator ) ) 3) 4 4) 3

4 3. Statement (a): During simple harmonic oscillation kinetic energy converted in potential energy and vice versa. Statement (b): otal mechanical energy of simple harmonic oscillator is directly proportional to square of the frequency of oscillation. Statement (c): Simple harmonic oscillator obeys the law of conservation of energy. Statement (d): otal mechanical energy of oscillator is directly proportional to a square of the amplitude of the oscillation. ) a, b are true ) c, d are true 3) a, b, d are true 4) a, b, c, d are true 4. otal energy of particle performing S.H.M. depends on ) Amplitude, ime Period ) Amplitude, ime Period and Displacement 3) Amplitude, Displacement 4) ime Period, Displacement 5. he work done by the body which is in S.H.M, against the restoring force is stored in the form of ) K.E. ) P.E. 3) Both P.E. & K.E. 4) otal energy 6. he phase of simple harmonic motion at t =0 is called ) Phase constant ) Initial phase 3) Epoch 4) All the above 7. In S.H.M. at the equilibrium position a) K.E is minimum b) Acceleration is zero c) Velocity is maximum d) P.E is maximum ) All true ) b, c, d true 3) a, b, c true 4) a, b, d true

5 8. (A): he motion of sewing needle is an example for SHM. (R): A liquid is taken in U-tube. Liquid in one limb is pressed and released It executes SHM. ) A and R are true but R is not the explanation for A. ) A and R are true R is the explanation for A. 3) A is true R is false. 4) A is false R is correct. 9. (A): he phase difference between displacement and velocity in SHM is (R): he displacement is represented by y = A sin wt. ) A and R true and R is correct explanation for A. ) A and R are true and R is not correct explanation for A. 3) A is true R is false. 4) A is false R is true. 0. When a body in SHM match the items in column A with that in column B. Item - I Item - II a) Velocity is maximum e) At half of the amplitude b) Kinetic energy is 3/4 th of total energy f) At the mean position c) P.E. is 3/4 th of total energy g) At extreme position d) Acceleration is maximum h) At 3 times amplitude

6 ) a - f, b - e, c - h, d - g ) a - e, b - f, c - g, d - h 3) a - g, b - h, c - e, d - f 4) a - h, b -e, c - f, d e. When a body in SHM match the statements in column A with that in column B. Column - I Column II a) Velocity is maximum e) At half of the amplitude b) Kinetic energy is 3/4 th of total energy f) At the mean position c) P.E. is 3/4 th of total energy g) At extreme position d) Acceleration is maximum h) At ) a - f, b - e, c - h, d - g ) a - e, b - f, c - g, d - h 3) a - g, b - h, c - e, d - f 4) a - h, b -e, c - f, d e 3 times amplitude. he time period of oscillation of the particle in SHM is ''. hen match the following. Column - I a) 3 8 th of oscillation from extreme position e) 3 b) 3 8 th of oscillation from mean position f) 3 Column II c) 5 8 th of oscillation from extreme position g) 7 d) 5 th of oscillation from mean position h) 5 8

7 ) a - e ; b- g ; c - f ; d - h ) a - f; b - h ; c - e ; d - g 3) a - f ; b - e ; c - h ; d - g 4) a - e ; b - f ; c - g ; d h 3. A): he displacement time graph for a particle in SHM is sine curve, when the motion begins from mean position. R): he displacement of a particle in SHM is given by y = A sin ωt ) A and R true and R is correct explanation for A. ) A and R are true and R is not correct explanation for A. 3) A is true R is false. 4) A is false R is true. 4. A): In damped vibrations, Amplitude of oscillation decreases. R): Damped vibrations indicate loss of energy due to air resistance. ) A and R true and R is correct explanation for A. ) A and R are true and R is not correct explanation for A. 3) A is true R is false. 4) A is false R is true. 5. A): SHM is an example of varying velocity and varying acceleration. R): For a particle performing SHM in non-viscous medium its total energy is constant. ) A and R true and R is correct explanation for A. ) A and R are true and R is not correct explanation for A. 3) A is true R is false.

8 4) A is false R is true. 6. he time period of a particle performing linear SHM is s. What is the time taken by it to make a displacement equal to half its amplitude? ) sec ) sec 3) 3sec 4) 4sec 7. he equation motion of a particle in S.H.M is a + 6 x = 0. In the equation a is the linear acceleration (in m/sec ) of the particle at a displacement x in meter. he time period of S H M in seconds is ) 4 ) 3) 4) 8. he displacement of a particle executing SHM is given by Y = 0 sin (3t + /3) m and t is in seconds. he initial displacement and maximum velocity of the particle are respectively ) 5 3m and 30m/sec ) 5m and 5 3 m/sec 3) 5 3 m and 30 m/sec 4) 0 3 m and 30 m/sec 9. A particle is vibrating in SHM with amplitude of 4cm. At what displacement from the equilibrium position it has half potential and half kinetic ) cm ) cm 3) cm 4) cm t 30. A particle moves according to the law x = a cos in the time interval between t = 0 to t = 3 sec is. he distance covered by it ) a ) 3a 3) 4 a 4) a 3. For a body in S.H.M the velocity is given by the relation v = he maximum acceleration is 44 6x m/sec. ) m/sec ) 6 m /sec 3) 36 m/sec 4) 48 m/sec

9 3. wo SHMs are represented by the equations y = 0 sin (3pt+ /4) and y = 5 [sin 3 t+ 3 cos3t]. heir amplitudes are in the ratio ) : ) : 3) :3 4) : 33. A body executing SHM at a displacement x its PE is E, at a displacement Y its PE is E. he P.E at a displacement (x + y) is ) E E E = ) E = E + E 3) E = E + E 4) E = E E 34. An object is attached to the bottom of a light vertical spring and set vibrating. he maximum speed of the object is 5 cm / sec and the period is 68 m sec. he amplitude of the motion in centimeter is ) 3 ) 3).5 4) he angular velocities of three bodies in SHM are ω ω ω 3 with their respective amplitudes as A A A 3. If all three bodies have same mass and velocity then ) A ω = A ω = A 3 ω 3 ) A ω = A ω = A 3 ω 3 3) A ω = A ω = A 3 ω 3 4) A ω = A ω = A 3 ω Four simple harmonic vibrations x = 8 sin ωt, x = 6 sin ( ωt + / ), x 3 = 4 sin 3 ( ωt + ) and x 4 = sin ωt + are superimposed on each other. he resulting amplitude is ) 0 ) 8 3) 4 4) 4

10 37. he displacement of a particle executing S.H.M from its mean portion is given by x = 0.5 sin (0 t +.5) cos (0 t +.5). he ratio of the maximum velocity to the maximum acceleration of the body is given by ) 0 ) 0 3) 0 4) he total mechanical energy of a harmonic oscillator of amplitude m and force constant 00 N/m is 50J. hen ) he minimum P E is Zero ) he maximum P E is 00 J 3) he minimum P E is 50 J 4) he maximum P E is 50 J 39. A particle of mass m is attached to a spring of spring constant ω o. An external force F(t) proportional to cos ω t ( ω ω o ) is applied to the oscillator. he time displacement of the oscillator will be proportional to m ( ω ω ) ) 0 m ( ) ) ω 0 +ω ( ) 3) m ω 0 +ω ( ) 4) m ω0 ω 40. A body executes SHM under the action of force F with a time period 4/5 sec. If the force is changed to F to execute SHM with time period (3/5) sec. If the both the forces F and F act simultaneously in the same direction on the body, its time period in seconds is (in see) ) 5 ) 5 3) 5 4 4) 5 4. A particle is executing simple harmonic motion along a straight line 8cm long. While passing through mean position its velocity is 6cm/s. Its time period will be () 0.57 sec ().57 sec (3) 5.7 sec (4) sec

11 4. A particle of mass 0.8 kg is executes S.H.M. its amplitude is.0m and time period is 7 sec. he velocity of the particle, at the instant when its displacement is 0.6m will be () 3 m/s () 3. m/s (3) 0.3 m/s (4) Zero Key ) ) 4 3) 3 4) 4 5) 4 6) 7) 8) 9) 4 0) 4 ) ) 3) 4 4) 5) 6) 4 7) 3 8) 9) 0) ) ) 3) 4) 5) 6) 7) 8) 9) 4 30) 3) 4 3) 4 33) 34) 3 35) 36) 3 37) 38) 3 39) 4 40) 4) 4) 6. Y = A cos ωt A = A cos wt cos( ω t) = wt = 3 t = t = / 6 3 Hints

12 7. a = 6 x ω 6 a = = ω x ω = 4 = 4 = = 4 8. t = 0 y = 0 sin = 5 3m 3 Vmax = ω A= 0 3 = 30 m/ sec 9. K.E. = P. E. mω ( A x ) = mω x A - x = x A = x = x = A / A 4 x = = = cm 30. x = acos t = acosωt 3. ω = / and = 4 sec = Distance covered will be = 3a V = 44 6x = 6(9 x ) V = 4 3 x

13 V = ω A x amax = ω A= (4 ) 3 = 48 m/ sec 3. y = 0sin (3 t+ / 4) 3 y = 5 sin3 t. + cos 3 t 33. [ ] y = D sin 3 t cos / 3 + sin / cos3 t y = Dsin(3 t+ /3) A: A = : PE E = mω x E x x E y x+ y E E From () and (), E = E + E 34. V max = A V max = A = A A =.5 cm 3

14 35. V = A ω A ω = A ω = A 3 ω A = 4 + u 0.5 sinθ cosθ x = 0.5 x = sin θ 0.5 x= sin(0 t+ 3) x = A sin ( ωt + φ) A w = = Aw w 0 A = 4 units 38. E of the particle is SHM = ka = 00 = 00J Mechanical energy = 50J at mean position the minimum PE is 39. Equation of displacement given by x = A sin ( ωt + φ) F0 F0 Where A= = m ( ω ω ) m( ω ω0 ) 0 Here damping effect is considered to be zero = 50J A m ( ω ω ) 0

15 40. 4 F = mω A= m A F F F + F + = = + 3 = sec 5 = sec 5 Vm = ωa= a a = = =.57 s V 6 m V = ω a x V = a x 7 = = 3. m/ s