Unit 3.2 Vibrations

Question 1

Define period, T of an oscillation.

Answer 1

It is the time for one complete cycle.

Question 2

Define Simple harmonic motion (SHM).

Answer 2

It occurs when an object moves such that its acceleration is always directed toward a fixed point and its proportional to its distance from the fixed point.`

Question 3

Give the formula for force, F relating to spring constant, k.

Answer 3

F = -kx

Question 4

Give the formula for acceleration, a relating to spring constant, k.

Answer 4

a = -(k/ m)x

Question 5

Give the formula for angular frequency, ω.

Answer 5

ω^2 = k / m

Question 6

Give the symbol for maximum displacement and state what it is.

Answer 6

A- amplitude of the oscillation

Question 7

State the formula for maximum velocity, vₘₐₓ relating to angular velocity, ω.

Answer 7

Vₘₐₓ = ωA

Question 8

State the formula for maximum acceleration, aₘₐₓ relating to angular velocity, ω.

Answer 8

aₘₐₓ = ω²A

Question 9

What is the angle ε?

Answer 9

Phase constant

Question 10

What does (ωt + ε) in the equation x = A cos(ωt + ε) represent?

Answer 10

The phase of the oscillation.

Question 11

State the equation for angular velocity, ω relating to spring constant, k.

Answer 11

ω = √(k/m)

Question 12

State the equation for frequency, f relating to spring constant, k.

Answer 12

f = (1 / 2π)√(k/m)

Question 13

State the equation for period, T relating to spring constant, k.

Answer 13

T = 2π √(m/k)

Question 14

State the equation for angular velocity, ω relating to spring constant, k for a 2 spring system.

Answer 14

ω = √((k₁ + k₂) / m)

Question 15

State the equation for period, T for a simple pendulum.

Answer 15

T = 2π √(l/g)

Question 16

Define free oscillations.

Answer 16

These occur when an oscillatory system is displaced and released.

Question 17

Define damping.

Answer 17

The dying away, due to resistive forces, of the amplitude of free oscillations.

Question 18

State the energy at an equilibrium point in an oscillating system.

Answer 18

zero for potential energy

Question 19

State the equation for displacement in an oscillating system.

Answer 19

x = A cosωt

Question 20

State the equation for velocity in an oscillating system.

Answer 20

v = -Aω sinω

Question 21

State the equation for acceleration in an oscillating system.

Answer 21

a = -Aω² cosωt

Question 22

State 3 types of damping.

Answer 22

1. Under- damping
2. Over- damping
3. Critical damping

Question 23

What is meant by under- damping?

Answer 23

Degree of damping is light.

Question 24

State the equation for an under- damped system.

Answer 24

x = A₀e⁻λᵗ cos(ωt + ε)