A S.H.M. has amplitude ‘a’ and  time period T. The maximum velocity will be -

(1) $\frac{4a}{T}$           

(2) $\frac{2a}{T}$

(3) $2\mathrm{\pi }\sqrt{\frac{\mathrm{a}}{\mathrm{T}} }$       

(4) $\frac{2\mathrm{\pi a}}{T}$                       

Two particles P and Q start from origin and execute Simple Harmonic Motion along X-axis with same amplitude but with periods 3 seconds and 6 seconds respectively. The ratio of the velocities of P and Q when they meet is -

(1)  1 : 2                 

(2)  2 : 1

(3)  2 : 3                 

(4)  3 : 2

The amplitude of a particle executing SHM is 4 cm. At the mean position the speed of the particle is 16 cm/sec. The distance of the particle from the mean position at which the speed of the particle becomes $8\sqrt{3}cm/sec$
$$ will be

(1) $2\sqrt{3}cm$             

(2) $\sqrt{3}cm$

(3) 1 cm                   

(4) 2 cm

The maximum velocity of a simple harmonic motion represented by $y=3 \sin \left(100t+\frac{\mathrm{\pi }}{6}\right)$ is given by

(1)   300       

(2)   $\frac{3\mathrm{\pi }}{6}$

(3)   100         

(4)   $\frac{\mathrm{\pi }}{6}$

The displacement equation of a particle is $x=3\sin 2t+4\cos 2t$ The amplitude and maximum velocity will be respectively

(a)       5, 10       (b)         3, 2

c)         4, 2        (d)         3, 4

The instantaneous displacement of a simple pendulum oscillator is given by $x=A \cos \left(\omega t+\frac{\mathrm{\pi }}{4}\right)$ . Its speed will be maximum at time

(1)$\frac{\mathrm{\pi }}{4\omega }$                   

(2) $\frac{\mathrm{\pi }}{2\omega }$

(3) $\frac{\mathrm{\pi }}{\omega }$                   

(4) $\frac{2\mathrm{\pi }}{\omega }$        

The displacement of a particle moving in S.H.M. at any instant is given by $y=a \sin$$\omega t$ . The acceleration after time $t=\frac{T}{4}$ (where T is the time period) -

1. $a\omega$                         

2.$-a\omega$

3. $a{\omega }^2$                         

4.  $-a{\omega }^2$

The amplitude of a particle executing S.H.M. with frequency of 60 Hz is 0.01 m. The maximum value of the acceleration of the particle is

(a)      $144{\mathrm{\pi }}^2\mathrm{m}/{\sec }^2$        (b)     $144m/se{c}^2$

c)      $\frac{144}{{\mathrm{\pi }}^2}m/se{c}^2$           (d)     $288{\mathrm{\pi }}^2\mathrm{m}/{\sec }^2$   

The displacement of an oscillating particle varies with time (in seconds) according to the equation $y\left(cm\right)=\sin \frac{\mathrm{\pi }}{2}\left(\frac{t}{2}+\frac{1}{3}\right)$ .The maximum acceleration of the particle is approximately 

(1) $5.21 cm/s^2$           

(2) $3.62 cm/s^2$

(3) $1.81 cm/s^2$           

(4) $0.62 cm/s^2$