The displacement of a particle is represented by the equation $$y= 3 \cos \left(\dfrac{\pi}{4}-\omega t \right)$$. The motion of the particle is:

 1 simple harmonic with period $$\dfrac{2\pi}{\omega}$$. 2 simple harmonic with period $$\dfrac{\pi}{\omega}$$. 3 periodic but not simple harmonic. 4 non-periodic.

Subtopic:  Simple Harmonic Motion |
64%
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The displacement of a particle is represented by the equation  $$y =\sin^{3}~\omega t$$. The motion is:
1. non-periodic.
2. periodic but not simple harmonic.
3. simple harmonic with period $$2\pi / \omega$$.
4. simple harmonic with period $$\pi / \omega$$.

Subtopic:  Simple Harmonic Motion |
69%
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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 $$a_1 = -2x$$
Subtopic:  Simple Harmonic Motion |
71%
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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.
Subtopic:  Simple Harmonic Motion |
55%
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A particle is acted simultaneously by mutually perpendicular simple harmonic motion $$x=a \text{cos}𝜔𝑡$$ and $$y = a\text{sin} 𝜔 𝑡$$. The trajectory of motion of the particle will be:

1. an ellipse

2. a parabola

3. a circle

4. a straight line

Subtopic:  Simple Harmonic Motion |
63%
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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 $$\sqrt{a^{2}+b^{2}}$$
Subtopic:  Simple Harmonic Motion |
88%
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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.
Subtopic:  Simple Harmonic Motion |
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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 $$\mathrm{x\text-}$$projection of the radius vector of the rotating particle $$P$$ will be:

1. $$x \left( t \right) = B$$ $$\text{sin} \left(\dfrac{2 πt}{30}\right)$$

2. $$x \left( t \right) = B$$ $$\text{cos} \left(\dfrac{πt}{15}\right)$$

3. $$x \left( t \right) = B$$ $$\text{sin} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)$$

4. $$x \left( t \right) = B$$ $$\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)$$

Subtopic:  Simple Harmonic Motion | Phasor Diagram |
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The equation of motion of a particle is $$x =a \text{cos} ( \alpha t )^{2}$$. The motion is:

1. periodic but not oscillatory

2. periodic and oscillatory

3. oscillatory but not periodic

4. neither periodic nor oscillatory

Subtopic:  Simple Harmonic Motion |
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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. $$\dfrac{\pi }{2}$$ s
3. $$2\pi$$ s
4. $$\dfrac{\pi }{4}$$ s

Subtopic:  Simple Harmonic Motion |
85%
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