5.3 Oscillations

Question 1

Considering a spring oscillating, give the
definitions of the following:
Displacement
Amplitude
Period
Frequency

Answer 1

● Displacement - distance from the equilibrium position
(vector)
● Amplitude - maximum displacement
● Period - time taken for a complete oscillation
● Frequency - number of oscillations per second

Question 2

State the equation relating angular frequency and
time period.

Answer 2

⍵ = 2π/T

Question 3

What are the conditions for SHM?

Answer 3

● Acceleration must be directly proportional
to displacement and in the opposite
direction:
(a ∝ -𝑥)
● It must act towards equilibrium.

Question 4

What are the two main examples of systems
which undergo SHM?

Answer 4

1. A mass-spring system
2. A pendulum

Question 5

What is the constant of proportionality linking
acceleration and displacement?

Answer 5

• ⍵^2

Question 6

What is 𝑥 as a function of t and ⍵?

Answer 6

𝑥 = Acos⍵t or 𝑥 = Asin⍵t

Question 7

What is 𝑥 as a function of t and ⍵?

Answer 7

𝑥 = Acos⍵t or 𝑥 = Asin⍵t

Question 8

True or false: velocity is maximum when
displacement is maximum.

Answer 8

False.
The velocity is minimum at the amplitude of
oscillation, as the object changes direction.
Velocity is maximum when the object passes through
the equilibrium position.

Question 9

True or false: velocity is maximum when
displacement is maximum.

Answer 9

False.
The velocity is minimum at the amplitude of
oscillation, as the object changes direction.
Velocity is maximum when the object passes through
the equilibrium position.

Question 10

How can you calculate the maximum speed
using ⍵ and A?

Answer 10

v = ⍵A

Question 11

What is damping?

Answer 11

Damping is the process by which the amplitude
of the oscillations decreases over time. This is
due to energy loss to resistive forces such as
drag or friction.

Question 12

explain the difference
between light damping, heavy damping and
critical damping.

Answer 12

Light damping occurs naturally (e.g. pendulum
oscillating in air), and the amplitude decreases
exponentially (but time period remains
constant as A and T are independent). When
heavy damping occurs (e.g. pendulum
oscillating in water) the amplitude decreases
dramatically. In critical damping (e.g. pendulum
oscillating in treacle) the object is stopped in
as short a time as possible without
overshooting equilibrium.

Question 13

What is the difference between free and forced
oscillations?

Answer 13

When an object oscillates without any external forces being
applied, it oscillates at its natural frequency. This is known as
free oscillation. Forced oscillation occurs when a periodic
driving force is applied to an object, which causes it to
oscillate at a particular frequency.

Question 14

What is resonance?

Answer 14

When the driving frequency of the external force applied to
an object is the same as the natural frequency of the object,
resonance occurs. This is when the amplitude of oscillation
rapidly increases, and if there is no damping, the amplitude
will continue to increase until the system fails. As damping
is increased, the amplitude will decrease at all frequencies,
and the maximum amplitude occurs at a lower frequency.