A particle executes simple harmonic motion. Let P be a point near the mean position and Q be a point near an extreme. The speed of the particle at P is larger than the speed at Q. Still the particle crosses P and Q equal number of times in a given time interval. Does it make you unhappy?
Answers
Answer ⇒ No, It does not make me unhappy.
Explanation ⇒ A Particle following the Simple Harmonic Motion, will be having the zero velocity at the extreme position.
This is because, As per as the Formula of the velocity,
v² = ω²(A² - x²)
where, ω is the angular frequency of the S.H.M. and A is the Amplitude and x is the distance which the particle in S.H.M Travels from the mean position.
Now, x = A, at extreme.
∴ v² = ω²(A² - A²)
∴ v = 0
This means, it comes to rest at the extreme positions.
This means, Velocity of Particle at P is greater than that of the velocity at Q as what said by mathematical expression.
But Still Particle goes to the Point Q, since, motion is Simple Harmonic and not the Uniform motion. And the motion towards the less velocity and vice versa is all due to the Inertia of Motion.
Hope it helps.