Oscillations

Question 1

What are the two conditions required for an object to oscillate with SHM?

Answer 1

• The restoring force is directly proportional to the displacement
• The restoring force always acts towards the equilibrium position

Question 2

What is angular frequency?

Answer 2

A measure of the rate of rotation of an object

Question 3

Give two equations for angular frequency.

Answer 3

w = 2pi/T
w = 2pi*f

Question 4

What are the two types of oscillations that an object can experience?

Answer 4

• Free oscillations
• Forced oscillations

Question 5

What is the frequency of a freely oscillating object equal to?

Answer 5

The object’s natural frequency

Question 6

What is resonance?

Answer 6

Resonance is where the amplitude of oscillations of an object drastically increases due to gaining an increased amount of energy from the driving force. This occurs when the driving frequency equals the natural frequency of the object

Question 7

What can be said about an object undergoing resonance?

Answer 7

The object will be oscillating at its maximum ampltidue and the rate of energy transfer is at a maximum

Question 8

What is damping?

Answer 8

Damping occurs when energy is lost from an oscillating system due to an external force acting on it

Question 9

What are the three types of damping?

Answer 9

1. Light damping
2. Critical damping
3. Heavy damping

Question 10

What is critical damping?

Answer 10

When the damping causes the object to return to the equilibirum position in the quickest time possible without oscillating

Question 11

State the equation for the total energy stored in a simple harmonic oscillator.

Answer 11

Energy stored = 1/2 kA^2
k is the spring constant and A is the amplitude

Question 12

If the displacement graph looked like a cos graph what would the veloctity time graph look like?

Answer 12

A negative sin graph

Question 13

If the displacement graph looked like a cos graph what would the acceleration time graph look like?

Answer 13

A negative cos graph

Question 14

What is the difference between free and forced oscillations?

Answer 14

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

Question 15

How can time period be calculated for a mass spring system?

Answer 15

T = 2π sqrt (m/k)
“T equals two pi times the square root of m( mass of object) over k(spring constant)”

Question 16

How can time period be calculated for a pendulum?

Answer 16

T = 2π sqrt (l/g)
“T equals 2 pi times the square root of l(length of string) over g (gravitational field strength)”

Question 17

How can you calculate the maximum acceleration of a SHM system?

Answer 17

a (max) = w^2A
the maximum amplitude is equal to the angular velocity squared multiplied by the amplitude

Question 18

How can you calculate the maximum velocity of a SHM system?

Answer 18

v (max) = wA = 2πfA
Maximum velocity = angular velocity x Ampltiude

Question 19

Is the kinetic energy at maximum or minimum as the object passes the equilibrium position?

Answer 19

Maximum

Question 20

Why must you use small angles for the pendulum equation to be valid?

Answer 20

It is an approximation as it assumes a straight path. Therefore we must use a small angle

Question 21

What does a pendulum undergo for a moment as it passes its equilibirum position?

Answer 21

Circular motion ( tension supplies the centripetal force)

Question 22

How will damping affect an amplitude-frequency graph?

Answer 22

The maximum, the resonance, is less (so moved down) and occurs at a lower frequency so moves left