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Practice each question, then open the answer or worked solution.
The displacement of a particle is represented by the equation y = 3 cos(π/4 – 2ωt). The motion of the particle is
a) simple harmonic with period 2p/w
b) simple harmonic with period π/ω
c) periodic but not simple harmonic
d) non-periodic
The correct answer is b) simple harmonic with period π/ω
The displacement of a particle is represented by the equation y = sin3 ωt. The motion is
a) non-periodic
b) periodic but not simple harmonic
c) simple harmonic with period 2π/ω
d) simple harmonic with period π/ω
The correct answer is c) simple harmonic with period 2π/ω
The relation between acceleration and displacement of four particles is given below:
a) ax = +2x
b) ax = +2x2
c) ax = -2x2
d) ax = -2x
Which one of the particles is executing simple harmonic motion?
The correct answer is d) ax = -2x
Motion of an oscillating liquid column in a U-tube is
a) periodic but not simple harmonic
b) non-periodic
c) simple harmonic and time period are independent of the density of the liquid
d) simple harmonic and time period are directly proportional to the density of the liquid
The correct answer is c) simple harmonic and time period is independent of the density of the liquid
A particle is acted simultaneously by mutually perpendicular simple harmonic motions x = a cos ωt and y = a sin ωt. The trajectory of motion of the particle will be
a) an ellipse
b) a parabola
c) a circle
d) a straight line
The correct answer is c) a circle
The displacement of a particle varies with time according to the relation y = a sin ωt + b cos ωt
a) the motion is oscillatory but not SHM
b) the motion is SHM with amplitude a + b
c) the motion is SHM with amplitude a2 + b2
d) the motion is SHM with amplitude √a2 + b2
The correct answer is d) the motion is SHM with amplitude √a2 + b2
Four pendulums A, B, C, and D are suspended from the same elastic support as shown in the figure. A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse displacement,
a) D will vibrate with maximum amplitude
b) C will vibrate with maximum amplitude
c) B will vibrate with maximum amplitude
d) all the four will oscillate with equal amplitude
The correct answer b) C will vibrate with maximum amplitude
Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution, and the initial position are indicated in the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is
a) x(t) = B sin (2πt/30)
b) x(t) = B cos (πt/15)
c) x(t) = B sin (πt/15 + π/2)
d) x(t) = B cos (πt/15 + π/2)
The correct answer a) x(t) = B sin (2πt/30)
The equation of motion of a particle is x = a cos (αt)2. The motion is
a) periodic but not oscillatory
b) periodic and oscillatory
c) oscillatory but not periodic
d) neither periodic nor oscillatory
The correct answer c) oscillator but not periodic
A particle executing SHM has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2. The period of oscillation is
a) πs
b) π/2 s
c) 2 πs
d) π/t s
The correct answer a) πs