Oscillations

Question 1

periodic motion:

Answer 1

Motion which repeats itself after regular intervals of time

Question 2

Oscillatory motion:

Answer 2

Motion in which an object moves to and fro in a repetitive manner about a fixed point in a definite interval of time.

Question 3

What is SHM?

Answer 3

Type of oscillatory motion, in which:
1. The particle moves in a single dimension
2. The particle oscillates to and fro about a fixed mean position (where Fnet=0)
3. The net force on the particle always gets directed towards the equilibrium position
4. The magnitude of the net force is always proportional to the displacement of the particle from the equilibrium position at that instant.

Question 4

F(net)=

Answer 4

Fnet=−kx

Question 5

a=

Answer 5

a=−kx/m
a=−ω²x

Question 6

x(t)=

Answer 6

x(t)=Asin(ωt+ϕ)

Question 7

Amplitude:

Answer 7

Maximum displacement on either side of the equilibrium position

Question 8

Time Period:

Answer 8

Time taken to complete one cycle
T=2π/ω=2π(√m/k)

Question 9

ω=

Answer 9

ω=√m/k

Question 10

Frequency:

Answer 10

number of oscillations completed in one second.

Question 11

nyu(freq)=

Answer 11

ν=ω/2π
=½π√k/m

Question 12

Phase:

Answer 12

State of a particle with respect to its position and direction of motion at that particular instant
Phase=(ωt+ϕ)

Question 13

ϕ is called ________ of the particle or phase constant.

Answer 13

initial phase

Question 14

At any instant t, v(t)=

Answer 14

v(t)=Aωcos(ωt +ϕ)

Question 15

At any position x, v(x)=

Answer 15

v(x)=±ω√A²−x²

Question 16

velocity has maximum magnitude at

Answer 16

The equilibrium position.

Question 17

At any instant t, a(t)=

Answer 17

a(t)=ω²A sin(ωt+ϕ)

Question 18

At any position x, a(x)=

Answer 18

a(x)=ω²x

Question 19

Acceleration is always directed towards

Answer 19

equilibrium position

Question 20

The magnitude of acceleration is minimum at

Answer 20

Equilibrium position and maximum at extremes

Question 21

K=

Answer 21

K=½mω²(A²-x²)
=½mω²A²cos²(ωt+ϕ)

Question 22

K(max)=

Answer 22

Kmax=½mω²A²

Question 23

U(x)=

Answer 23

U(x)=½kx²=½mA²ω²sin²(ωt+ϕ)

Question 24

T.E.=

Answer 24

T.E.=½kA²=½mA²ω²

Question 25

To understand whether a motion is S.H.M:

Answer 25

Locate the equilibrium position mathematically by balancing all the forces on it. Displace the particle from the mean position in the direction of oscillation. Determine net force on it and check if it is towards the mean position. Express net force as a proportional function of its displacement If step (c) and step (d) are proved then it is a simple harmonic motion.

Question 26

Systems executing SHM:

Answer 26

vertical & horizontal spring: T=2π√m/k Simple Pendulum: T=2π√ℓ/g

Question 27

v(t)=

Answer 27

-₩Asin(₩t + ø)

Question 28

a(t)=

Answer 28

-₩²x(t)