Why we Cannot use equation of motion in case of acceleration varies with time?

No, the equations are only valid for constant acceleration. The reason is that the acceleration being constant was an inherent assumption you made when you did the derivations of the equations. You would need to use calculus to derive equations for the case of time-varying acceleration.

Is SHM and circular motion same?

Simple harmonic motion can be visualized as the projection of uniform circular motion onto one axis. The phase angle ωt in SHM corresponds to the real angle ωt through which the ball has moved in circular motion.

Can we use the equation V U at in SHM or not?

Notes: The equation of motion ‘v = u +at’ can be applied only when the acceleration is constant. It cannot be applied in the cases of simple harmonic motion and circular motion.

What is the difference between simple harmonic motion and the motion of a pendulum?

A good example of the difference between harmonic motion and simple harmonic motion is the simple pendulum. The simple pendulum undergoes harmonic motion, however for small angles of oscillation it does approximately undergo simple harmonic motion. Harmonic motion would just be any motion that is periodic.

Can the equation of kinematics be used when the acceleration varies with time if not what form would these equations take?

No, the equations of are not applicable when the acceleration varies with time.

When can we say that an object is exhibiting a simple harmonic motion?

Simple harmonic motion can be considered the one-dimensional projection of uniform circular motion. If an object moves with angular speed ω around a circle of radius r centered at the origin of the xy-plane, then its motion along each coordinate is simple harmonic motion with amplitude r and angular frequency ω.

How periodic motion is different from harmonic motion?

The main difference between simple harmonic motion and periodic motion is that periodic motion refers to any type of repeated motion whereas simple harmonic motion (SHM) refers to a specific type of periodic motion where the restoring force is proportional to the displacement.

Can the equation of motion be used when acceleration is zero?

Equation of motion are applicable when the acceleration is constant. Thus, equation of motion is zero as zero is also a constant.

What is the relation between SHM and uniform circular motion?

The connection between uniform circular motion and SHM. The amplitude is simply the maximum displacement of the object from the equilibrium position. So, in other words, the same equation applies to the position of an object experiencing simple harmonic motion and one dimension of the position of an object experiencing uniform circular motion.

Does acceleration oscillate in simple harmonic motion?

Acceleration in SHM The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force.

What are the solutions of simple harmonic motion differential equation?

The solutions of simple harmonic motion differential equation are given below: x = Asinωt, it is the solution for the particle when it is in its mean position point ‘O’ in figure (a). x0​ = Asinϕ, it is the solution for the particle when it is in any other position but not in the mean position in figure (b).

How do you find the velocity of a harmonic motion?

Velocity in SHM. In simple harmonic motion, the velocity constantly changes, oscillating just as the displacement does. When the displacement is maximum, however, the velocity is zero; when the displacement is zero, the velocity is maximum. It turns out that the velocity is given by: Acceleration in SHM