Oscillations

Question 1

Restoring force in SHM

Answer 1

F= -kx

• k: force constant
• x: displacement from mean position

Question 2

What is amplitude?

Answer 2

Max displacement from mean position

Question 3

What is Time period ?

Answer 3

Time taken for one complete oscillation

Question 4

What is frequency?

Answer 4

No: of oscillations in unit time

ν = 1/T

• ν: frequency
• T: time period

Question 5

Angular frequency (ω)

Answer 5

ω = 2πν = 2π/T

Question 6

How is uniform circular motion and SHM related?

Answer 6

• uniform circular motion is periodic but not simple harmonic
• projection of a body in uniform circular motion about its diameter is SHM

Question 7

What is phase?

Answer 7

It represents the state of vibration of an oscillating body
- (ωt + Φ₀)
- Φ: phase constant

Question 8

Displacement in SHM

Answer 8

• Y=Asinωt: if particle starts from mean position
• x=Acosωt: if particle starts from extreme position
• Y=Asin(ωt ± Φ₀): in general from mean position

Question 9

Velocity in SHM

Answer 9

V= Aωcosωt
OR
V= ω √ (A² - Y²)

Question 10

Acceleration in SHM

Answer 10

a= -Aω²sinωt
OR
a = -ω²Y

Question 11

Force in SHM

Answer 11

(F = ma)

• F= -mAω²sinωt
• F = -mω²Y

Question 12

When is velocity max and min in SHM?

Answer 12

• Max at mean position (Aω)
• Min at extreme position (0)

Question 13

When is acceleration max and min in SHM?

Answer 13

• Max at extreme (ω²A)
• Min at mean (0)

Question 14

When is P.E max and min in SHM?

Answer 14

• Max at extreme (½mω²A²)
• Min at mean (0)

Question 15

When is KE max and min in SHM?

Answer 15

-Max at mean (½mω²A²)
- Min at extreme (0)

Question 16

Where is TE in SHM max?

Answer 16

Total energy in SHM is constant everywhere.
½mω²A²

Question 17

Eqn of P.E in SHM

Answer 17

½mω²Y²

Question 18

Eqn for K.E in SHM

Answer 18

½mω²(A² - Y²)

Question 19

Differential eqn of SHM

Answer 19

(d²Y/dt²) + ω²Y = 0

• ω² = k/m

Question 20

Time period of simple pendulum

Answer 20

T= 2π √(l/g)

Question 21

Second’s pendulum

Answer 21

Has time period two seconds

Question 22

Time period of spring pendulum

Answer 22

T= 2π √(m/k)

Question 23

Spring constant in series combination

Answer 23

1/Kₑբբ = 1/K₁ + 1/K₂

Question 24

Spring constant in parallel combination

Answer 24

Kₑբբ= K₁ + K₂

Question 25

Spring constant and length of spring relation

Answer 25

K × l = constant (hooke's law) - K: spring constant - l: length of spring

Question 26

Graph between length of pendulum and time period is a

Answer 26

Parabola

Question 27

If 'f' is the frequency of oscillation. What's the frequency of oscillation of K.E and P.E?

Answer 27

- Frequency of K.E = 2f - Frequency of P.E = 2f

Question 28

How does the time period (T) of simple pendulum vary in a period

Answer 28

**T/12 sec** - 0 --> A/2 - A/2 --> 0 **T/6 sec** - A/2 --> A - A --> A/2

Question 29

Displacement and velocity of SHM differ in phase by how much

Answer 29

π/2

Question 30

Average K.E and P.E in linear SHM are

Answer 30

Equal