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

An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is -

1. 4 Mg/K         

2. 2 Mg/K

3. Mg/K             

4. Mg/2K

The period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\theta$, is given by -

1.   $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{gcos\theta }}}$               

2.  $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{gsin}\theta }}$

3.  $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g} }}$                     

4. $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{gtan\theta }}}$

The displacement of a particle varies according to the relation x = 4(cosp$\mathrm{\pi }$t + sinp$\mathrm{\pi }$t). The amplitude of the particle is

1. 8

2. -4

3. 4

4. $4\sqrt{2}$

The time period of a simple pendulum of length L as measured in an elevator descending with acceleration $\frac{\mathrm{g}}{3}$ is

1. $2\mathrm{\pi }\sqrt{\frac{3\mathrm{L}}{\mathrm{g}}}$

2. $\mathrm{\pi }\sqrt{\left(\frac{3\mathrm{L}}{\mathrm{g}}\right)}$

3. $2\mathrm{\pi }\sqrt{\left(\frac{3\mathrm{L}}{2\mathrm{g}}\right)}$

4. $2\mathrm{\pi }\sqrt{\frac{2\mathrm{L}}{3\mathrm{g}}}$

The period of a simple pendulum measured inside a stationary lift is found to be T. If the lift starts accelerating upwards with acceleration of g/3 then the time period of the pendulum is

1. $\frac{\mathrm{T}}{\sqrt{3}}$

2. $\frac{\mathrm{T}}{3}$

3. $\frac{\sqrt{3}}{2}\mathrm{T}$

4. $\sqrt{3}\mathrm{T}$

A simple harmonic wave having an amplitude a and time period T is represented by the equation $y=5 \mathrm{sin\pi }\left(t+4\right)$m Then the value of amplitude (a) in (m) and time period  (T) in second are       

1.   $a=10, T=2$   

2. $a=5, T=1$

3.    $a=10, T=1$    

4. $a=5, T=2$

If the length of a pendulum is made \(9\) times and the mass of the bob is made \(4\) times, then the value of time period will become:
1. \(3T\)
2. \(\dfrac{3}{2}{T}\)
3. \(4{T}\)
4. \(2{T}\)