Oscillations

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Common Misconceptions

7 min read

- What you are getting from a statement might not be necessarily true. Let's burst some of the common misconceptions

MYTH: Necessary and sufficient condition of S.H.M. is that force is proportional to displacement.
FACT: Necessary and sufficient condition of S.H.M. is that the restoring force is proportional to displacement.

MYTH:In S.H.M, kinetic energy is equal to potential energy.
FACT: In S.H.M, the average kinetic energy is equal to average potential energy if average is taken over a complete period and the potential energy in resting position is zero.

MYTH: In S.H.M. of amplitude A, the time taken to traverse from x = 0 to A/2 and from x = A/2 to A is the same.
FACT: In S.H.M. of amplitude A, the time (

t_{1}

) taken to traverse from x = 0 to A/2 is less than the time (

t_{2}

) taken from x = A/2 to A, because the velocity of particle at mean position is maximum at it goes on decreasing towards extreme position is maximum at it goes on decreasing towards extreme position. In fact,

t_{1} = t_{2} / 2

MYTH: The motion of particle executing uniform circular path is S.H.M.
FACT: The motion of particle executing uniform circular path is not S.H.M.; but the motion of projection of perpendicular drawn from instantaneous positions of particle executing uniform circular motion is S.H.M.

MYTH: The time period of a simple pendulum does not depend upon size and mass of bob.
FACT: The time period of a simple pendulum does not depend upon mass, but depends on the size of bob; because by increasing size of bob, the effective length of pendulum increases.

MYTH: In forced oscillations, the amplitude resonance and velocity (or energy) resonance occurs at the same driving frequency of force which is equal to the frequency of free oscillations of the body.
FACT: In forced oscillations, the amplitude resonance occurs at a slightly lower frequency than the natural frequency of oscillations of the body while the velocity (or energy) resonance occurs when the frequency of driving force is equal to the natural frequency of oscillations of the body.
When a driving force is applied to an oscillating system at a frequency near the natural frequency of the system, the amplitude of the oscillation becomes large. This relatively large response of an oscillator to being driven at a frequency that is near its natural frequency is called resonance.

MYTH: When a spring of spring constant K is divided into n equal parts, the spring constant of each part reduces to K/n.
FACT: When a spring of spring constant K is divided into n equal parts, the spring constant of each part increases to nK.