Identify the correct definition:

From the given functions, identify the function which represents a periodic motion:

1.  $e^{\omega t}$

2.  ${\log }_e\left(\omega t\right)$

3.  $\sin \omega t+\cos \omega t$

4.  $e^{-\omega t}$

The angular velocities of three bodies in simple harmonic motion are ${\omega }_1,$ ${\omega }_2,$ ${\omega }_3$ with their respective amplitudes as $A_1,$ $A_2,$ $A_3$. If all the three bodies have the same mass and maximum velocity, then:

An SHM has an amplitude \(a\) and  a time period \(T.\) The maximum velocity will be:
1. \({4a \over T}\)       
2.  \({2a \over T}\)
3. \({2 \pi \over T}\)
4. \({2a \pi \over T}\)  

The equation of motion of a particle is \({d^2y \over dt^2}+Ky=0 \) where \(K\) is a positive constant. The time period of the motion is given by: 

Displacement versus time curve for a particle executing SHM is shown in the figure. Choose the correct statement/s.

The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
                

1. 25 Hz
2. 50 Hz
3. 12.25 Hz
4. 33.3 Hz

If the time of mean position from amplitude (extreme) position is 6 seconds, then the frequency of SHM will be:

The equation of an SHM is given as y=3sinωt + 4cosωt where y is in centimeters. The amplitude of the SHM will be?

Two simple harmonic motions of angular frequency 100 rad s ^-1 and 1000 rad $s^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration will be:
1. 1:10
2. 1:10²
3. 1:10³                               
4. 1:10⁴