The displacement of a particle is represented by the equation y = . The motion is
1. non-periodic
2. periodic but not simple harmonic
3. simple harmonic with period 2
4. simple harmonic with period
The relations between acceleration and displacement of four particles are given below. Which one of the particles is executing simple harmonic motion?
1. \(a_1 = +2x\)
2. \(a_1= +2x^2\)
3. \(a_1= -2x^2\)
4. \(a_1 = -2x\)
Motion of an oscillating liquid column in a U-tube is
1. | periodic but not simple harmonic |
2. | non-periodic |
3. | simple harmonic and time period is independent of the density of the liquid |
4. | simple harmonic and time period is directly proportional to the density of the liquid |
A particle is acted simultaneously by mutually perpendicular simple harmonic motion x=acos and y = asin. The trajectory of motion of the particle will be:
1. an ellipse
2. a parabola
3. a circle
4. a straight line
The displacement of a particle varies with time according to the relation, \(y=a~\text{sin} \omega t+b~\text{cos} \omega t.\)
1. | the motion is oscillatory but not SHM |
2. | the motion is SHM with amplitude \(a+b\) |
3. | the motion is SHM with amplitude \(a^{2}+b^{2}\) |
4. | the motion is SHM with amplitude \(\sqrt{a^{2}+b^{2}}\) |
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 large than A. If A is given a transverse displacement,
1. D will vibrate with maximum amplitude
2. C will vibrate with maximum amplitude
3. B will vibrate with maximum amplitude
4. All four will oscillate with equal amplitude
The figure shows the circular motion of a particle. The radius of the circle, the period, the 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 will be:
1.
2.
3.
4.
The equation of motion of a particle is x =. The motion is:
1. periodic but not oscillatory
2. periodic and oscillatory
3. oscillatory but not periodic
4. neither periodic nor oscillatory
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:
1. \(\pi \) s
2. \(\frac{\pi }{2}\) s
3. \(2\pi\) s
4. \(\frac{\pi }{4}\) s
When a mass \(m\) is connected individually to two springs \(S_1\) and \(S_2,\) the oscillation frequencies are \(\nu_1\) and \(\nu_2.\) If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be:
1. \(v_2+v_2\)
2. \(\sqrt{v_1^2+v_2^2}\)
3. \(\frac{1}{v_1}+\frac{1}{v_1}^{-1}\)
4. \(\sqrt{v_1^2-v_2^2}\)