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. $1:10^{4}$

A point performs simple harmonic oscillation of period T and the equation of motion is given by x= a sin $\left(\omega t +\pi /6\right)$.After the elapse of what fraction of the time period the velocity of the point will be equal to half to its maximum velocity?

1.  $\frac{T}{8}$

2.  $\frac{T}{6}$

3. $\frac{\mathrm{ T}}{3}$

4 $\frac{T}{\mathrm{ 12}}$