Class 11 Physics - Chapter Oscillations NCERT Solutions | Figures 14.29 correspond to two circular
Figures 14.29 correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure.
Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each case.
( 1 ) For time period, T = 4 s
Amplitude, A = 3 cm
At time, t = 0, the radius vector OB makes an angle π/2 with the positive x-axis, i.e., Phase angel Φ = + π/2
Therfore, the equation of simple harmonic motion for the x-projection of OB, at time t is:
x = A cos [ 2πt/T + Φ ]
= 3 cos [2πt/4 + π/2 ]
= -3sin ( πt/2 )
= -3sin ( πt/2 ) cm
( 2 ) Time period, T = 8 s
Amplitude, A = 2 m
At time t = 0, OB makes an angle π with the x-axis, in the anticlockwise direction. Thus, phase angle, Φ = + π
Therefore, the equation of simple harmonic motion for the x-projection of OB, at time t is:
x = A cos [ 2πt/T + Φ ]
= 2 cos [ 2πt/8 + π ]
= -2 cos ( πt/4 )
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Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (ω is any positive constant):
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(b) sin3 ωt
(c) 3 cos (π/4 - 2ωt)
(d) cos ωt + cos 3ωt + cos 5ωt
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A spring having with a spring constant 1200 N m-1 is mounted on a horizontal table as shown in Fig. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.
Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.
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Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
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(d) general vibrations of a polyatomic molecule about its equilibrium position.
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A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is
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(b) at the end B,
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