Which one of the following equations does not represent SHM, x = displacement, and t = time? Parameters a, b and c are the constants of motion.

(1) x = a sin bt

(2) x = a cos bt + c

(3) x = a sin bt + c cos bt

(4) x = a sec bt + c cosec bt

Subtopic:  Types of Motion |
 74%
From NCERT
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The bob of a simple pendulum of length L is released at time t = 0 from a position of small angular displacement. Its linear displacement at time t is given by :

(1) X=a sin2πLg×t

(2) X=a cos2πgL×t

(3) X=a singL×t

(4) X=a cosgL×t

Subtopic:  Simple Harmonic Motion |
From NCERT
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A particle in SHM is described by the displacement function x(t)=A cos(ωt+ϕ), ω=2π/T. If the initial (t = 0) position of the particle is 1 cm, its initial velocity is π cm s-1 and its angular frequency is πs-1, then the amplitude of its motion is:

(1) π cm

(2) 2 cm

(3) 2 cm

(4) 1 cm

Subtopic:  Simple Harmonic Motion |
 59%
From NCERT
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A particle starts SHM from the mean position. Its amplitude is 'a' and total energy E. At one instant its kinetic energy is 3E/4. Its displacement at this instant is :

(1) y=a/2

(2) y=a2

(3) y=a3/2

(4) y = a

Subtopic:  Energy of SHM |
 73%
From NCERT
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A particle is vibrating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, is its energy half potential and half kinetic?

(1) 1 cm

(2) 2 cm

(3) 3 cm

(4) 22 cm

Subtopic:  Energy of SHM |
 79%
From NCERT
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A body of mass 500 g is attached to a horizontal spring of spring constant 8 π2Nm-1. If the body is pulled to a distance of 10 cm from its mean position, then its frequency of oscillation is :

(1) 2 Hz

(2) 4 Hz

(3) 8 Hz

(4) 0.5 Hz

Subtopic:  Simple Harmonic Motion |
 70%
From NCERT
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Two springs of force constants k and 2k are connected to a mass m as shown below. The frequency of oscillation of the mass is:

(1) 12πk/m

(2) 12π2k/m

(3) 12π3km

(4) 12πmk

Subtopic:  Combination of Springs |
 86%
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A weightless spring that has a force constant k oscillates with frequency n when a mass m is suspended from it. The spring is cut into equal halves and a mass 2m is suspended from one part of the spring. The frequency of oscillation will now become:

1. n

2. 2n

3. n2

4. n(2)1/2

Subtopic:  Simple Harmonic Motion |
 65%
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An object suspended from a spring exhibits oscillations of period T. Now, the spring is cut in two halves and the same object is suspended with two halves as shown in the figure. The new time period of oscillation will become :

1. T22

2. T2

3. T2

4. 2T

Subtopic:  Combination of Springs |
 58%
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A mass 1 kg suspended from a spring whose force constant is 400 Nm-1, executes simple harmonic oscillation. When the total energy of the oscillator is 2 J, the maximum acceleration experienced by the mass will be:

1. 2 ms-2

2. 4 ms-2

3. 40 ms-2

4. 400 ms-2

Subtopic:  Energy of SHM |
 76%
From NCERT
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