Question

discuss S. H. M. as special case of circular motion and derive the expression for displacement and velocity of a body executing SHM​

Answer 1

Answer:

Velocity and Acceleration in Simple Harmonic Motion

A motion is said to be accelerated when its velocity keeps changing. But in simple harmonic motion, the particle performs the same motion again and again over a period of time. Do you think it is accelerated? Let’s find out and learn how to calculate the acceleration and velocity of SHM.

JOIN NOW

Search for a topic

Physics > Oscillations > Velocity and Acceleration in Simple Harmonic Motion

Oscillations

Velocity and Acceleration in Simple Harmonic Motion

A motion is said to be accelerated when its velocity keeps changing. But in simple harmonic motion, the particle performs the same motion again and again over a period of time. Do you think it is accelerated? Let’s find out and learn how to calculate the acceleration and velocity of SHM.

Suggested Videos

ArrowArrow

ArrowArrow

Introduction to Periodic Motion H

SHM as a projection of circular motion I H

VST Simple Harmonic Motion Problem 4 and its Solution

Solve

Questions

Two simple harmonic are represented by the equations { y }_{ 1 }=0.1sin\left( 100\pi t+\dfrac { \pi }{ 3 } \right) y

1

=0.1sin(100πt+

3

π

) and { y }_{ 2 }=0.1y

2

=0.1 cosxt. The phase difference of the velocity of particle 1, with respect to the velocity of particle 2 is -

1 Verified answer

A Simple harmonic oscillator has a period of 0.01{\text{ }}s0.01 s and an amplitude of 0.2\,m.0.2m. The magnitude of the velocity in m se{c^{ - 1}}sec

−1

at the mean position will be

1 Verifi

The velocity of a particle in SHM at the instant when it is 0.60.6 cm away from the mean position is 44 cm /sec. If the amplitude of vibration is 11 cm then its velocity at the instant when it is 0.80.8cm away from the mean position is:

Acceleration in SHM

We know what acceleration is. It is velocity per unit time. We can calculate the acceleration of a particle performing S.H.M. Lets learn how. The differential equation of linear S.H.M. is d2x/dt2 + (k/m)x = 0 where d2x/dt2 is the acceleration of the particle, x is the displacement of the particle, m is the mass of the particle and k is the force constant. We know that k/m = ω2 where ω is the angular frequency.

Therefore, d2x/dt2 +ω2 x = 0

Hence, acceleration of S.H.M. = d2x/dt2 = – ω2 x

The negative sign indicated that acceleration and displacement are in opposite direction of each other. Equation I is the expression of acceleration of S.H.M. Practically, the motion of a particle performing S.H.M. is accelerated because its velocity keeps changing either by a constant number or varied number.

Take a simple pendulum for example. When we swing a pendulum, it moves to and fro about its mean position. But after some time, it eventually stops and returns to its mean position. This type of simple harmonic motion in which velocity or amplitude keeps changing is damped simple harmonic motion.