# Oscillations – Physics 12

## Oscillations – Physics 12

A particle moving along the X-axis, executes simple harmonic motion then the force acting on it is given by

(a)– A kx

(b)Acos (kx)

(c)Aexp (– kx)

(d)Akx where, Aand k are positive constants.

2.A particle, with restoring force proportional to displacement and resistve force proportional to velocity is subjected to a force F sin ω0. If the amplitude of the particle is maximum for ω= ω1 and the energy of the particle is maximum forω= ω2, then

(a) ω1= ω0 and ω2 ≠ ω0

(b)ω1= ω0 and ω2 = ω0

(c)ω1≠ ω0 and ω2 ≠ ω0

(d)ω1 ≠ ω0 and ω2 ≠ ω0

3.A masses suspended from a two coupled springs, connected in series. The force constant for springs are k1and k2. The time period of the suspended mass will be

(a)T=2π√m/k1-k2

(b) T=2π√mk1k2/k1+k2

(c)T=2π√m/k1+k2

(d)T=2π√m(k1+k2)/k1+k2

4.The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of π results in the displacement of the particle along

(a)circle

(b)figures of eight

(c)straight line

(d)ellipse

5.The angular velocity and the amplitude of a simple pendulum is x and a respectively. At a displacement x from the mean position if its kinetic energy is Tand potential energy is V, then the ratio of T to Vis

(a)(a²-x²ω²)/x²ω²

(b)x²ω²/(a²-x²ω²)

(c)(a²-x²)/x²

(d)x²/(a²-x²)

6.A body is executing S.H.M. When the displacements from the mean position are 4cmand 5 cm, the corresponding velocities of the body are 10 cm per sec and 8 cm per sec. Then the time period of the body is

(a)2πsec

(b)π/2 sec

(c)πsec

(d)(3π/2)sec

7.A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a, then the time period is given by T=2π√(l/g), where g is equal to

(a)g

(b)g – a

(c)g+ a

(d)√(g²+a²)

8.If a simple harmonic oscillator has got a displacement of 0.02 m and acceleration equal to2.0 m/s² at any time, the angular frequency of the oscillator is equal to

(a)10 rad/s

(b)0.1 rad/s

(c)100 rad/s

(d)1rad/s

9.A simple harmonic oscillator has an amplitude Aand time period T. The time required by it to travel from x = A to x= A/2 is

(a)T/6

(b)T/4

(c)T/3

(d)T/2

10.A wave has S.H.M (Simple Harmonic Motion)whose period is 4 seconds while another wave which also possess SHM has its period 3seconds. If both are combined, then the resultant wave will have the period equal to

(a)4 seconds

(b)5 seconds

(c)12 seconds

(d)3 seconds

11.A body executes S.H.M 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 ?

(a)A/4

(b)A/2

(c)3A/4

(d)Some other fraction of A.

12.Which one of the following is a simple harmonic motion?

(a)Ball bouncing between two rigid vertical walls

(b)Particle moving in a circle with uniform speed

(c)Wave moving through a string fixed at both ends

(d)Earth spinning about its own axis.

13.A particle is subjected to two mutually per-pendicular simple harmonic motions such that its x and Y coordinates are given by x= 2sin ωt; 2sin(ωt+π/4) The path of the particle will be[1(a)a straight line

(b)a circle

(c)an ellipse

(d)a parabola

14.In a simple harmonic motion, when the displacement is one-half the amplitude, what fraction of the total energy is kinetic?

(a)0

(b)1/4

(c)1/2

(d)3/4

15.A linear harmonic oscillator of force constant 2× 10³+³N/m and amplitude 0.01 m has a total mechanical energy of 160 J. Its

(a)maximum potential energy is 160 J

(b)maximum potential energy is 100 J

(c)minimum potential energy is zero

(d)minimum potential energy is 100 J

16.A particle starts simple harmonic motion from the mean position. Its amplitude is A and time period is T.What is its displacement when its speed is half of its maximum speed

(a)√2/3A

(b)√3/A

(c)2/√3A

(d)A/√2

17.If the length of a simple pendulum is increased by 2%, then the time period

(a)increases by 2%

(b)decreases by 2%

(c)increases by 1%

(d)decreases by 1%

18.Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will be

(a)a circle

(b)an ellipse with the major axis along y-axis

(c)an ellipse with the major axis along x-axis

(d)a straight line inclined at 45º to the x-axis

19.A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will

(a)first increase and then decrease

(b)first decrease and then increase

(c)go on increasing

(d)go on decreasing

20.Two simple pendulums of length 5m and 20m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed ……. oscillations

(a)5

(b)1

(c)2

(d)3

21.A mass m is vertically suspended from a spring of negligible mass; the system oscillates with frequency n. What will be the frequency of the system, if a mass 4mis suspended from the same spring?

(a)n/4

(b)4n

(c)n/2

(d)2n

22.The time period ofa simple pendulum is 2seconds. If its length is increased by 4-times, then its period becomes

(a)16 s

(b)12 s

(c)8 s

(d)4 s

23.A particle executing S.H.M. has amplitude 0.01mand frequency 60 Hz. The maximum acceleration of the particle is

(a)144 π²m/s²

(b)120 π²m/s²

(c)80 π²m/s²

(d)60 π²m/s²

24.Masses MAand MBhanging from the ends of strings of lengths LAand LB are executing simple harmonic motions. If their frequencies are fA =2fB, then

(a)LA= 2LBand MA= MB/2

(b)LA = 4LBregardless of masses

(c)LA= LB/4 regardless of masses

(d)LA= 2LBand MA= 2MB

25.Two simple harmonic motions act on a particle.These harmonic motions are x= A cos (ωt+ δ), y= A cos (ωt+ α) when δ=α+π/2, the resulting motion is

(a)acircle and the actual motion is clockwise

(b)an ellipse and the actual motion is counterclockwise

(c)an elllipse and the actual motion is clockwise

(d)acircle and the actual motion is counterclockwise26.A simple pendulum has a metal bob, which is negatively charged.If it is allowed to oscillate above a positively charged metallic plate,then its time period will

(a)increase

(b)decrease

(c)become zero

(d)remain the same

27.There is a body having mass m and performingS.H.M. with amplitude a. There is a restoring force F = –kx. The total energy of body depends upon

(a)k, x

(b)k, a

(c)k, a, x

(d)k, a, v

28.A body of mass M, executes vertical SHM with periods t1and t2, when separately attached to spring A and spring B respectively. The period of SHM, when the body executes SHM, as shown in the figure ist0. Then BAM

(a)t0–1 = t1–1 + t2–1

(b)t0= t1+ t2

(c)t02= t12+ t22

(d)t0–2= t1–2+ t2–2

29.The amplitude of a pendulum executing damped simple harmonic motion falls to 1/3 the original value after 100 oscillations. The amplitude falls to Stimestheoriginal value after 200 oscillations,whereSis

(a)1/9

(b)1/2

(c)2/3

(d)1/6

30.A particle is executing a simple harmonic motion of amplitude a. Its potential energy is maximum when the displacement from the position of the maximum kinetic energy is

(a)0

(b)±a

(c)±a/2

(d)– a/2

31.A particle of mass M oscillates with simple harmonic motion between points x1and x2, the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph.

(a)X1X2O

(b)X1X2O

(c)X1X2O

(d)X1X2O

32.The potential energy of a simple harmonic oscillator when the particle is half way to its endpoint is

(a)1/2E

(b)2/3E

(c)1/8E

(d)1/4E

where E is the total energy

33.In case of a forced vibration, the resonance wave becomes very sharp when the

(a)quality factor is small

(b)damping force is small

(c)restoring force is small

(d)applied periodic force is small

34.Thetimeperiodofa mass suspended from spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

(a)2T

(b)T/4

(c)2

(d)T/4

35.Which one of the following statements is true fourth-speed v and the acceleration a of a particle executing simple harmonic motion ?

(a)When vis maximum, a is zero

(b)When v is maximum, a is maximum

(c)Value of a is zero, whatever may be the value of v

(d)When v is zero, a is zero

36.Two springs of spring constants k1and k2 are joine din series. The effective spring constant of the combination is given by

(a)k1k2/(k1 + k2)

(b)k1k2

(c)(k1 + k2) /2

(d)k1 + k2

37.A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4cm/s. The frequency of its oscillation is

(a)4Hz

(b)3 Hz

(c)2Hz

(d)1 Hz

38.The potential energy of a long spring when stretched by2 cm is U. If the spring is stretched by 8 cm, the potential energy stored in it is

(a)8 U

(b)16 U

(c)U/ 4

(d)4 U

39.The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

(a)π

(b)0.707π

(c)zero

(d)0.5π

40.The particle executing simple harmonic motion has a kinetic energy Kocos² ωt The maximum values of the potential energy and the total energy are respectively

(a)K0/2 and K0

(b)K0and 2K0

(c)K0and K0

(d)0and 2K0

41.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 plan 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 = 10m/s2)?m

(a)10.0 cm

(b)any value less than 12.0cm

(c)4.0 cm

(d)8.0 cm

42.A particle executes simple harmonic oscillation with an amplitude a. The period of oscillationisT. The minimum time taken by the particle to travel a half of the amplitude from the equilibrium position is

(a)T/8

(b)T/12

(c)T/2

(d)T/4

43.Two simple harmonic motions of angular frequency 100 and 1000 rad s-¹have the same displacement amplitude. The ratio of their maximum accelerations is:

(a)1 : 10

(b)1 : 10²

(c)1 : 10³

(d)1 : 10²+²

44.A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin(ωt +π/6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?

(a)T/8

(b)T/6

(c)T/3

(d)T/12

45.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)πa/T

(b)3π²a/T

(c)πa√3/T

(d)πa√3/2T

46.Which one of the following equations of motion represents simple harmonic motion?

(a)Acceleration = –k(x + a)

(b)Acceleration = k(x +a)

(c)Acceleration= kx

(d)Acceleration = – k0x + k1x² where k, k0, k1and a are all postive

47.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:

(a)2Mg/k

(b)4 Mg/k

(c)Mg/2k

(d)Mg/k

48.The displacement of a v particle along the x-axis is given by x = a sin²ωt. The motion of the particle corresponds to:

(a)simple harmonic motion of frequency ω/π

(b)simple harmonic motion v of frequency 3ω/2π

(c)non simple harmonic motion

(d)simple harmonic motion of frequency ω/2π

49.The period of oscillation of a mass M suspended from a spring of negligible mass is T. If along with it another mass Mis also suspended, the period of oscillation will now be

(a)T

(b)T⁄√2

(c)2T

(c)√2T

50.A particle of mass m is released from rest and follows a parabolic path as shown.Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time(x)mV(x)0

(a)x(t)0t

(b)x(t)0t

(c)0tx(t)

(d)x(t)0t

51.Out of the following functions, lines side representing motion of a particle, which represents SHM?

(A)y=sinωt-cosωt

(B)y= sin³ ωt

(C)y=5cos(3π/4-3ωt)

(D)y = 1+ωt+ω²t²

(a)Only (A)

(b)Only (D) does not represent SHM

(c)Only (A) and (C)

(d)Only (A) and (B)

52.Two particles are oscillating along two close parallel lines side by y side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when theirdisplacement is half of the amplitude. The mean positions of the two particles lie on a straigh tline perpendicular to the paths of the two particles. The phase difference is

(a)0

(b)2π/3

(c)π

(d)π/6

53.The damping force on anoscillator is directly proportional to the velocity. The units of the constant of proportionality are :

(a)kgms-¹

(b)kgms-²

(c)kgs-¹

(d)kgs

54.The equation of asimple harmonic wave is given by y=3sinπ/3(50t-x) Where x and y are in meters and t is in seconds.The ratio of maximum particle velocity to thewave velocity is

(a)2π

(b)3/2π

(c)3π

(d)2/3π

55.Aparticle of mass m oscillates along x-axisaccording to equation x = a sin ωt. The natureofthe graph between momentum and displacementof the particle is

(a)straight line passing through origin

(b)circle

(c)hyperbola

(d)ellipse

- Ans(1)
- Ans(3)
- Ans(4)
- Ans(3)
- Ans(3)
- Ans(3)
- Ans(4)
- Ans(1)
- Ans(1)
- Ans(3)
- Ans(2)
- Ans(3)
- Ans(3)
- Ans(4)
- Ans(1,2)
- Ans(2)
- Ans(3)
- Ans(1)
- Ans(1)
- Ans(3)
- Ans(3)
- Ans(4)
- Ans(1)
- Ans(3)
- Ans(4)
- Ans(2)
- Ans(2)
- Ans(4)
- Ans(1)
- Ans(2)
- Ans(2)
- Ans(4)
- Ans(2)
- Ans(4)
- Ans(1)
- Ans(1)
- Ans(4)
- Ans(2)
- Ans(4)
- Ans(3)
- Ans(1)
- Ans(2)
- Ans(2)
- Ans(4)
- Ans(3)
- Ans(1)
- Ans(4)
- Ans(1)
- Ans(4)
- Ans(1)
- Ans(3)
- Ans(2)
- Ans(3)
- Ans(2)
- Ans(4)

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