The motion of a particle varies with time according to the relation \(y= a\sin\omega t+ a\cos \omega t\). Then:

1.	the motion is oscillatory but not SHM.
2.	the motion is SHM with an amplitude \(a\sqrt{2}\).
3.	the motion is SHM with an amplitude \(\sqrt{2}\).
4.	the motion is SHM with an amplitude \(a\).

 The displacement of a particle executing SHM is given by y = 0.25 (sin 200t) cm. The maximum speed of the particles is:

1.  200 cm/sec

2.  100 cm/sec

3.  50 cm/sec

4.  0.25 cm/sec

Which of the following figure represents damped harmonic motion?

(i)
(ii)
(iii)
(iv)

1. (i) and (ii)

2. (iii) and (iv)

3. (i), (ii), (iii), and (iv)

4. (i) and  (iv)

The time period of a spring mass system at the surface of the earth is \(2~\text{s}.\) What will be the time period of this system on the moon where the acceleration due to gravity is \(\frac{1}{16}^\text{th}\) of the value of \(g\) on the earth's surface?

A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude?

1. $\frac{1}{2}s$

2. $\frac{1}{6}s$

3. $\frac{1}{4}s$

4. $\frac{1}{3}s$

The uniform stick of mass m length \(\text L\) is pivoted at the centre. In the equilibrium position shown in the figure, the identical light springs have their natural length. If the stick is turned through a small angle $\theta$, it executes SHM. The frequency of the motion is:

1. \(\frac{1}{2 \pi} \sqrt{\frac{6 K}{m}} \)

2. \(\frac{1}{2 \pi} \sqrt{\frac{3 K}{2 m}} \)

3. \(\frac{1}{2 \pi} \sqrt{\frac{3 K}{m}} \)

4. None of these