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Oscillations · Question 34

AIPMT 2011 (Prelims)MCQMedium📈 Topic in 38% papers+4−1
1

Out of the following functions representing motion of a particle which represents SHM (1) y = sin t - cos t (2) y = sin3 t (3) y = 5 cos ( 3 4 - 3 t ) (4) y = 1 + t + 2 t2

  1. Only (1)
  2. Only (4) does not represent SHM
  3. Only (1) and (3)
  4. Only (1) and (2)

Answer

(3) Only (1) and (3)

Solution

A motion is SHM only if it can be written as a single sine or cosine function of time, i.e. a = - 2 y.

(1) y = sin t - cos t

y = 2 sin ( t - 4 ) → SHM

(2) y = sin3 t = 3 sin t - sin 3 t4

sum of two SHMs of different frequencies → periodic but not SHM

(3) y = 5 cos ( 3 4 - 3 t ) → single cosine function of angular frequency 3 → SHM

(4) y = 1 + t + 2 t2 → grows without limit, not even periodic → not SHM

Only (1) and (3) represent SHM.

Answer: (3)

AIPMT 2011 (Prelims)

Keep practising — Oscillations

2

The displacement of a particle along the x-axis is given by x = a 2 . The motion of the particle corresponds to

  1. simple harmonic motion of frequency /
  2. simple harmonic motion of frequency 3 /2
  3. non simple harmonic motion
  4. simple harmonic motion of frequency /2
AIPMT 2010 (Prelims)
3

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

  1. T
  2. T 2
  3. 2T
  4. 2T
AIPMT 2010 (Prelims)
4

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

  1. aT
  2. 3 2 aT
  3. a 3T
  4. a 32T
AIPMT 2009
5

Which one of the following equations of motion represents simple harmonic motion ? where k, k0, k1 and a are all positive.

  1. Acceleration = -k(x + a)
  2. Acceleration = k(x + a)
  3. Acceleration = - 2x
  4. Acceleration = -k0x + k1x2
AIPMT 2009
6

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

  1. 1 : 103
  2. 1 : 104
  3. 1 : 10
  4. 1 : 102
AIPMT 2008
7

A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a ( t + /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?

  1. T/3
  2. T/12
  3. T/8
  4. T/6
AIPMT 2008
8

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

  1. T/8
  2. T/12
  3. T/2
  4. T/4
AIPMT 2007
9

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 pan 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 = 10 m/s2). [figure]

  1. 10.0 cm
  2. any value less than 12.0 cm
  3. 4.0 cm
  4. 8.0 cm
AIPMT 2007
10

The particle executing simple harmonic motion has a kinetic energy K0 2 t. The maximum values of the potential energy and the total energy are respectively

  1. K0/2 and K0
  2. K0 and 2K0
  3. K0 and K0
  4. 0 and 2K0
AIPMT 2007
11

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

  2. 0.707
  3. zero
  4. 0.5
AIPMT 2007

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