Question

Select wrong statement about simple harmonic motion
A. The body is uniformly accelerated
B. The velocity of the body changes smoothly at all instants
C. The amplitude of oscillation is symmetric about the equilibrium position
D. The frequency of oscillation is independent of amplitude

Answer 1

Hint:We must know the concept of “oscillation”. The motion is vibratory or oscillatory if a particle moves back and forth along the same path during a periodic motion. While every periodic motion is oscillatory, not all oscillatory motion is periodic.

Complete step by step solution:
Simple Harmonic Motion: Simple harmonic motion is when a particle oscillates up and down (back and forth) about a mean position (also known as equilibrium position) in such a way that a restoring force/ torque acts on the particle, which is proportional to displacement from mean position but acts in the opposite direction from displacement. It is known as a linear S.H.M. if the displacement is linear, and an angular S.H.M. if the displacement is angular.

S.H.M. related terms:
Amplitude: The amplitude of an oscillating particle is the largest displacement of that particle on either side of its mean location.
Time period: A particle's time period is the length of time it takes for one oscillation to complete.
Phase: The parameter used to represent a particle's deviation from its typical position is referred to as phase.
Frequency: The number of oscillations that are completed in a second is the frequency.

In Simple Harmonic Motion,
$a=-{{\omega }^{2}}x$
As a result, the acceleration 'a' here depends on 'x,' hence it is not constant.
$v=A\sin (\omega t+\phi )$
Since velocity is a sin function, its variations are smooth. About the mean, amplitude is symmetric. In SHM, frequency is dependent on duration rather than amplitude.

Hence, the option A is correct.

Note: The following describes the phase relationship in S.H.M. between displacement, velocity, and acceleration:
-By a phase $\dfrac{\pi }{2}$ radian, the velocity is ahead of the displacement.
-By a phase π radian, the acceleration is in front of the displacement.
-By a phase $\dfrac{\pi }{2}$ radian, the acceleration is ahead of the velocity.
-Whenever$x=\dfrac{A}{2}$, then $V = 0.86 \,V_{max}$ for velocity.