Oscillations (SHM) · JEE Main previous year questions

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2023 18 questions

Q562023 · 13 Apr 2023 · Shift 1· Numerical answer
At a given point of time the value of displacement of a simple harmonic oscillator is given as $y = A cos (3 0^{\circ})$ . If amplitude is $40 cm$ and kinetic energy at that time is $200 J$ , the value of force constant is $1.0 \times 1 0^{x} Nm^{- 1}$ . The value of $x$ is ___________.
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Answer: 4
Q312023 · 12 Apr 2023 · Shift 1
A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be
1. A.1 : 1
2. B.1 : 4
3. C.2 : 1
4. D.1 : 3
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Answer: D
Q392023 · 11 Apr 2023 · Shift 1
1. A.
2. B.
3. C.
4. D.
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Answer: C
Q342023 · 10 Apr 2023 · Shift 1
The energy of an electromagnetic wave contained in a small volume oscillates with
1. A.double the frequency of the wave
2. B.the frequency of the wave
3. C.half the frequency of the wave
4. D.zero frequency
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Answer: A
Q532023 · 10 Apr 2023 · Shift 2· Numerical answer
A rectangular block of mass 5 kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3.14 s. The maximum force exerted by spring on block is _________ N
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Answer: 20
Q432023 · 6 Apr 2023 · Shift 1
1. A. $2 π \frac{m}{K _{1} + K _{2}}$
2. B. $2 π \frac{m}{K _{1} - K _{2}}$
3. C. $\frac{1}{2 π} \frac{K _{1} + K _{2}}{m}$
4. D. $\frac{1}{2 π} \frac{K _{1} - K _{2}}{m}$
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Answer: A
Q572023 · 6 Apr 2023 · Shift 2· Numerical answer
A simple pendulum with length $100 cm$ and bob of mass $250 g$ is executing S.H.M. of amplitude $10 cm$ . The maximum tension in the string is found to be $\frac{x}{40} N$ . The value of $x$ is ___________.
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Answer: 101
Q422023 · 31 Jan 2023 · Shift 1
The maximum potential energy of a block executing simple harmonic motion is $25 J$ . A is amplitude of oscillation. At $A /2$ , the kinetic energy of the block is
1. A. $9.75 J$
2. B. $37.5 J$
3. C. $18.75 J$
4. D. $12.5 J$
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Answer: C
Q532023 · 30 Jan 2023 · Shift 1· Numerical answer
The general displacement of a simple harmonic oscillator is $x = A sin ω t$ . Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when $t = \frac{T}{β}$ . The value of $β$ is __________.
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Answer: 8
Q512023 · 29 Jan 2023 · Shift 1· Numerical answer
Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.
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Answer: 120
Q362023 · 29 Jan 2023 · Shift 2
Identify the correct statements from the following : A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. C. Work done by friction on a body sliding down an inclined plane is positive. D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero. E. Work done by the air resistance on an oscillating pendulum is negative. Choose the correct answer from the options given below :
1. A.A and C only
2. B.B and D only
3. C.B, D and E only
4. D.B and E only
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Answer: D
Q542023 · 29 Jan 2023 · Shift 2· Numerical answer
A particle of mass 250 g executes a simple harmonic motion under a periodic force $F = (- 25 x) N$ . The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ____ cm.
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Answer: 40
Q372023 · 25 Jan 2023 · Shift 1
T is the time period of simple pendulum on the earth's surface. Its time period becomes $x$ T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of $x$ will be :
1. A.4
2. B. $\frac{1}{2}$
3. C.2
4. D. $\frac{1}{4}$
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Answer: C
Q382023 · 25 Jan 2023 · Shift 1
Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately) (Take $g = 10 m s^{- 2}$ , radius of earth = 6400 km)
1. A.12 hours
2. B.1 hour 24 minutes
3. C.24 hours
4. D.1 hour 40 minutes
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Answer: B
Q322023 · 25 Jan 2023 · Shift 2
A particle executes simple harmonic motion between $x = - A$ and $x = + A$ . If time taken by particle to go from $x = 0$ to $\frac{A}{2}$ is 2 s; then time taken by particle in going from $x = \frac{A}{2}$ to A is
1. A.4 s
2. B.1.5 s
3. C.3 s
4. D.2 s
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Answer: A
Q522023 · 24 Jan 2023 · Shift 1· Numerical answer
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Answer: 5
Q362023 · 24 Jan 2023 · Shift 2
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : A pendulum clock when taken to Mount Everest becomes fast. Reason R : The value of g (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth. In the light of the above statements, choose the most appropriate answer from the options given below
1. A.Both A and R are correct but R is NOT the correct explanation of A
2. B.A is correct but R is not correct
3. C.Both A and R are correct and R is the correct explanation of A
4. D.A is not correct but R is correct
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Answer: D
Q592023 · 24 Jan 2023 · Shift 2· Numerical answer
A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of the oscillation increases by one second, the value of mass m is ___________ kg.
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Answer: 1