A particle of mass m is attached to three identical springs A, B and C each of force constant k a shown in figure. If the particle of mass m is pushed slightly against the spring A and released then the time period of oscillations is -

(a) $2\mathrm{\pi }\sqrt{\frac{2\mathrm{m}}{\mathrm{k}}}$          (b) $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{2\mathrm{k}}}$

(c) $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$            (d) $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{3\mathrm{k}}}$

              

                 

The graph shows the variation of displacement of a particle executing SHM with time. We infer from this graph that:

For a particle executing SHM the displacement \(x \) is given by, \(A\cos \omega t.\)  Identify the graph which represents the variation of potential energy (P.E.) as a function of time \(t\) and displacement \(x.\)

   
1. I, III
2. II, IV
3. II, III
4. I, IV

The velocity-time diagram of a harmonic oscillator is shown in the adjoining figure. The frequency of oscillation is

(1) 25 Hz           

(2) 50 Hz

(3) 12.25 Hz       

(4) 33.3 Hz

The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is

(1) 1 $\times$10² N/m               

(2) 150 N/m

(3) 0.667 $\times$ 10² N/m       

(4) 3 $\times$ 10² N/m

A body performs S.H.M. . Its kinetic energy K varies with time t as indicated by graph

(a)    (b) 

(c)      (d) 

The displacement of a body executing SHM is given by x= A sin (2$\mathrm{\pi }$t + $\mathrm{\pi }$/3). The first time from t = 0 when the velocity is maximum is :
1. 0.33 sec
2. 0.16 sec
3. 0.25 sec
4. 0.5 sec

The time period of a particle executing SHM is 8 sec. At t = 0 it is at the mean position. The ratio of the distance covered by the particle in the 1st second to the 2nd second is :

1. $\frac{1}{\sqrt{2} + 1}$

2. $\sqrt{2}$

3. $\frac{1}{\sqrt{2} }$

4. $\sqrt{2} + 1$

Two particles are in SHM in a straight line. Amplitude A and time period T of both the particles are equal. At time t = 0, one particle is at displacement Y₁ = + A and the other at Y₂ = -A/2, and they are approaching towards each other. After what time they cross each other?
1. T/3
2. T/4
3. 5T/6
4. T/6

Two particles execute SHM of the same amplitude of \(20\) cm with the same time period along the same line about the same equilibrium position. The maximum distance between the two is \(20\) cm. Their phase difference in radians is:
1. \(\frac{2\pi}{3}\)
2. \(\frac{\pi}{2}\)
3. \(\frac{\pi}{3}\)
4. \(\frac{\pi}{4}\)