This concept has been created as a Quick Silver Test Series . The idea is to generate 25 questions of all hot topics for JEE and AIEEE and help you brush up your concepts for the same. The first in the series is Simple Harmonic Motion. 'Owl the best'!

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Q1.Two point masses of 3.0 kg and 1.0 kg are attached to opposite ends of a horizontal spring whose spring constant is 300 Nm^–1 as shown in the figure. The natural vibration frequency of the system is about:

1. 4 Hz
2. 3 H
3. 2 Hz
4. 1 Hz


Q2.In a spring-mass system the length of the spring is L and it has a mass M attached to it and oscillates with an angular frequency w. The spring is then cut into two parts, one (A) with relaxed length aL and the other (B) with relaxed length (1 – a)L. The force constants of the two springs A and B are:
1.
2.
3.k and k
4.




Q3.Period of small oscillations in the two case is T₁ and T₂ respectively, then:

1.T₁ = T₂
2.T₁ < T₂
3.T₁ > T₂
4. cannot say anything


Q4.A body is performing linear SHM. If the acceleration and corresponding velocity of the body are a and v respectively, which of the following graphs is correct?
1.
2.
3.
4.



Q5.The displacement time graph of a particle executing SHM is shown in figure. Which of the following statement is false?
1.The velocity is maximum at
2.The acceleration is maximum at t = T
3.The force is zero at t = 3T/4
4. The potential energy equals the total oscillation energy at


Q6.In SHM, potential energy of a particle at mean position is E₁ and kinetic energy is E₂, then:
1.E₁ = E₂
2.
3.
4.


Q7.The potential energy of a particle of mass 2 kg in SHM is (9x²) J. Here x is the displacement from mean position. If total mechanical energy of the particle is 36 J. Then maximum speed of the particle is:
1.4 m/s 
2.2 m/s
3. 6 m/s
4. 10 m/s


Q8.The variation of PE of harmonic oscillator is as shown in figure. The spring constant is:



1. 1 x 10² N/m
2. 1.5 x 10² N/m 
3. 0.667 x 10² N/m
4.3 x 10² N/m

Q9.In the above question KE of particle at mean position is:
1.0.01 J  
2. 0.03 J
3. 0.04 J
4. 0.05 J


Q10.Two blocks connected by a spring rest on a smooth horizontal plane as shown in figure. A constant force F starts acting in the block m₂ as shown in the figure:
1. Length of spring increases continuously if m₁ > m₂
2.Block start performing SHM about centre of mass of the system, which moves rectilinearly with constant acceleration.
3. Blocks start performing oscillations about centre of mass of the system with increasing amplitude.
4. Acceleration of m₂ is maximum at initial moment of time only.




Q11.A cubical block of mass M vibrates horizontally with an amplitude of 4.0 cm and a frequency of 2.0 Hz. A small block of mass m is placed on the bigger block. In order that the smaller block does not slide on the bigger block, the minimum value of the coefficient of static friction between the two blocks is:
1.  0.36 
2. 0.40
3.  0.64
4. 0.72


Q12.The period of a particle executing SHM is 8s. At t = 0 it is at the mean position. The ratio of the distances covered by the particle in the 1^st second to the 2^nd second is:
1.
2.
3.
4.


Q13.Figure (a) shows a spring of force constant k fixed at one end and carrying a mass m at the other end placed on a horizontal frictionless surface. The spring is stretched by a force F. Figure (b) shows the same spring with both ends free and a mass x fixed at each free end. Each of the spring is stretched by the same force F. The mass in case (a) and the masses in case (b) are then released. Which of the following statement is true?

(a) While oscillating, the maximum extension of the spring is more in case (a) than in case (b)

(b) The maximum extension of the spring is the same in both cases

(c) The time period of oscillation is the same in both cases

(d) The time period of oscillation in case (a) is 2 times that in case (b)



Q14.The minimum phase difference between the two simple harmonic oscillation


and
1.
2.
3.
4.





Q15. A body is performing SHM with amplitude a and time period T. Variation of its acceleration (f) with time (t) is shown in figure. If at time t, velocity of the body is v, which of the following graphs is correct?

1.
2.
3.
4.


Q16.A particle is performing SHM with amplitude a and time period T. Its position x varies with time as shown in figure. If at time t, acceleration of the particle is f, which of the following graphs is/are correct?

1.
2.
3.
4.


Q17.A particle is performing SHM with amplitude a and time period T. Its acceleration f varies with time as shown in figure. If at time t, kinetic energy of the particle is K, which of the following graphs is correct?


1.
2.
3.
4.




Q18.A particle is performing SHM. Its kinetic energy K varies with time t as shown in figure. Then:




(a) period of oscillations of the particle is equal to T9o

(b) excess potential energy U of the particle varies with time t as shown in graph (a)

(c) excess potential energy U of the particle varies with time t as shown in graph (b)

(d) None of these –––––––––––––––––––––––––––––––––––––––––––––



Q19.A particle is performing SHM. If its displacement from mean position is x, corresponding resultant force on it is F and acceleration is a, which of the following graph is correct?

1.
2.
3.
4.


Q20.A particle is performing a linear SHM. If the acceleration and the corresponding velocity of the particle are a and v respectively, which of the following graphs is correct?
1.
2.
3.
4.


Q21.A body is performing linear SHM. If the acceleration and the corresponding velocity of the body are a and v respectively, which of the following graphs is INCORRECT?
1.
2.
3.
4.


Q22.One end of an ideal spring is connected with a smooth block with the other end with rear wall of driving cabin of a truck as shown in the figure. Initially, the system is at rest. If truck starts to accelerate with a constant acceleration then the block (relative to truck):
1.will remain stationary
2. will start oscillating with constant amplitude
3.will start oscillating with increasing amplitude
4. moves such that length of the spring first increases and then become constant






Q23.Two particles executes SHM of same amplitude and frequency along the same straight line. They pass one another when going in opposite directions, each time their displacement is half their amplitude. What is the phase difference between them?
1.60°
2.30°
3. 90°
4. 120°


Q24.A uniform rod of length l is suspended by an end is made to undergo small oscillations. What is the length of a simple pendulum which has the same time period as that of the rod?
1.l
2.l / 2
3.2l / 3 
4.l / 3




Q25.A particle of mass M is executing oscillations about the origin on the x – axis. Its potential energy is |U| = K |x|², where K is a positive constant. If the amplitude of oscillation is a, then its period T is:
1.
2.independent of a     
3.
4. proportional to a^3/2