What remains constant in a simple harmonic motion?

CONCEPT:

• Simple Harmonic Motion (SHM): Simple harmonic motion is a special type of periodic motion or oscillation where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
  • Example: Motion of an undamped pendulum, undamped spring-mass system.

The equation of SHM is given by:

Y = A Sin (ω t + θ)

Where A is amplitude, ω is the angular frequency, t is time and θ is the initial phase angle

The relation between time period (T) and natural frequency is given by:

T = 2π/ω 

Natural frequency is given by: \(\omega \; = \;\sqrt {\frac{k}{m}} \)

The velocity of particle in SHM;
\({\rm{V}} = {\rm{\omega }}\sqrt {{A^2} - {y^2}} \),

Where V = velocity, ω = angular velocity, A = amplitude and y = displacement.

Kinetic energy (KE) = ½ m V2

Potential energy = 1/2 k y²

EXPLANATION:

• From the above discussion, we can say that the time period is what remains constant in a simple harmonic motion. So option 2 is correct. 
• The kinetic energy and potential energy depends on the displacement (y) that varies with time, so they are not constant during the motion.