A particle executes linear simple harmonic motion with an amplitude of of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity  is equal to that of its acceleration. Then, its time period in seconds is 

1. $\sqrt{\frac{5}{\pi }}$

2.$\sqrt{\frac{5}{2\mathrm{\pi }}}$

3. $\frac{4\mathrm{\pi }}{\sqrt{5}}$

4. $\frac{2\mathrm{\pi }}{\sqrt{3}}$

A body mass m is attached to the lower end of a spring whose upper end is fixed. The spring has neglible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. The value of m in kg is-

1. $\frac{3}{4}$               

2. $\frac{4}{3}$

3. $\frac{16}{9}$               

4. $\frac{9}{16}$

When two displacements represented by y₁=asin(ωt) and y₂=bcos(ωt) are superimposed,the motion is -

1. not a simple harmonic

2. simple harmonic with amplitude a/b

3. simple harmonic with amplitude $\sqrt{a^{2 }+ b^2}$

4. simple harmonic with amplitude (a+b)/2

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are 

1.$\mathrm{ k}g m{s}^{-1}$                               

2.$\mathrm{ k}g m{s}^{-2}$

3. $kg s^{-1}$                                   

4. $kg s$

The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T.$ If along with it another mass $M$ is also suspended, the period of oscillation will now be:
1. $T$
2. $T/\sqrt{2}$
3. $2T$
4. $\sqrt{2} T$

Two simple harmonic motions of angular frequency $100~\text{rad s}^{-1}$ and $1000~\text{rad s}^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration will be:
1. $1:10$
2. $1:10^{2}$
3. $1:10^{3}$
4. $1:10^{4}$