Oscillations

Question 1

What is periodic motion?

Answer 1

Any motion that repeats itself over and over again at regular intervals of time

Question 2

Oscillatory Motion / Harmonic

Answer 2

Body moves back and forth repeatedly about its mean position

Question 3

Fourier theorem

Answer 3

Any arbitrary function F(t) with period T can be expressed as the unique combination of sine and cosine functions fn (t) and gn (t) with suitable coefficients

Question 4

Harmonic Functions

Answer 4

Periodic functions that can be represented by a sine or cosine curve

Question 5

Non-harmonic Functions

Answer 5

Periodic functions which cannot be represented by single sine or cosine function

Question 6

Simple Harmonic Motion

Answer 6

If it moves to and fro about a mean position under the action of a restoring force which is directly proportional to its displacement from the mean position and is always directed towards the mean position

Question 7

Prove to find the differential equation of SHM

Answer 7

-
d^x / dt^2 + (omega)^2 x = 0

Question 8

Find the of SHM:
1. Displacement
2. Time period

Answer 8

1. x = A cos(omega t + psi not)
2. T = 2pi (root m / k)

Question 9

Harmonic Oscillator

Answer 9

A particle executing simple harmonic motion

Question 10

Amplitude

Answer 10

Maximum displacement of the osciallating particle on either side of its mean position

Question 11

Oscillation

Answer 11

One complete back and forth motion of a particle starting and ending at the same point

Question 12

Angular frequency

Answer 12

Quantity obtained by multiplying frequency by a factor of 2pi

Question 13

Phase

Answer 13

Gives the state of the particle as regards its position and the direction of motion at that instant

Question 14

Initial phase / Epoch

Answer 14

Phase of a vibrating particle corresponding to time t = 0

Question 15

Circle of Reference

Answer 15

A circle of reference can refer to a circle used to establish the center of a component or to a circle used to describe the motion of a particle undergoing simple harmonic motion (SHM)

Question 16

Displacement formula from centre of circle

Answer 16

x = A cos (omega t + psi not)
A = amplitude
x = Displacement
omega t = angular frequency
psi not = initial phase

Question 17

Acceleration in SHM

Answer 17

a(t) = - omega ^2 A cos (omega t + psi not) = - omega ^2 x

Question 18

Acceleration amplitude

Answer 18

Acceleration amplitude is the maximum acceleration of an oscillating particle

Question 19

Acceleration amplitude formula

Answer 19

a max = omega^2 A = (2pi / T)^2 A

Question 20

acceleration in SHM

Answer 20

a(t) = omega ^2 A cos (omega t + pi)

Question 21

Kinetic Energy in SHM

Answer 21

KE = 1/2 m omega^2 A^2 sin^2 (omega t + psi not) = 1/2 m omega^2 (A^2 - x^2)

Question 22

Potential Energy in SHM

Answer 22

U = 1/2 kx^2 = 1/2 m omega^2 x^2 = 1/2 m omega^2 A^2 cos^2 (omega t + psi not)

Question 23

Total Energy in SHM

Answer 23

E = 1/2 k A^2 = 1/2 m omega^2 A^2 = 2 pi^2 m v^2 A^2

Question 24

Time period in SHM

Answer 24

T = 2pi root (m / k)

Question 25

Oscillation frequency for springs connected in parallel

Answer 25

mu = 1/2pi [root (k1 + k2) / m]

Question 26

Oscillation frequency for springs connected in series

Answer 26

mu = 1 / 2pi [root (k1k2 / m (k1 + k2))]

Question 27

Simple Pendulum

Answer 27

Consists of a point-mass suspended by a flexible, inelastic and weightless string from a rigid support of infinite mass

Question 28

Time period of a bob of simple pendulum

Answer 28

T = 2pi root (l / g)

Question 29

Free Oscillations

Answer 29

If a body, capable of oscillation, is slightly displaced from its position of equiliibrium and left to itself, it starts oscillating with a frequnecy of its own

Question 30

Damped Oscillations

Answer 30

Oscillations in which the amplitude decreases gradually with the passage of time