Oscillations

Question 1

What are oscillations?

Answer 1

They are to and for motion about an equilibrium value.

Question 2

Name example of dissociative forces that can stop an oscillation.

Answer 2

Frictional and viscous forces.

Question 3

What is the displacement of an object in an oscillating system?

Answer 3

It is the distance and direction of the body from its rest or equilibrium position.

Question 4

What is amplitude?

Answer 4

It is the maximum magnitude of displacement.

Question 5

What is one oscillation

Answer 5

Physical value has passed from one side of its equilibrium value to the other side and back again to its original value.

Question 6

What’s is frequency?

Answer 6

Number of complete oscillations per unit time.

Question 7

What is angular frequency?

Answer 7

It is the circular representation of frequency. One complete oscillation is represented by 2π. ω=2πf

Unit: rad s-1

Question 8

Relate period, frequency and angular frequency.

Answer 8

T = 1/f = 2π/ω

Question 9

What is phase?

Answer 9

It is the stage of position of an oscillating system within the complete cycle of an oscillation.

Question 10

How is phase expressed?

Answer 10

Fraction of T of as an angle where 2π is one cycle.

Question 11

What is phase difference between two oscillations of the same frequency?

Answer 11

It is the difference between the phases in oscillations.

Question 12

What is simple harmonic motion?

Answer 12

It is (to and fro) a motion in which the acceleration is proportional but opposite in direction to the displacement. 
a is directly proportional to -x

Question 13

How is SHM related to circular motion?

Answer 13

When an object is in uniform circular motion, the vertical component is taken into consideration. Take the - of the vertical component of centripetal acceleration ω^2r because acceleration is in the opposite direction in SHM and using x(vertical component) = rsinθ obtain their vertical component of acceleration.

Question 14

What is the equation for the definition of SHM?

Answer 14

a = -ω^2x

Question 15

ω^2 = ?

Answer 15

Restoring force per unit displacement/ inertia = k/m

Question 16

What are the equations for displacement, velocity and acceleration in terms of maximum displacement, velocity and acceleration?

Answer 16

x=x0sinωt
v=v0cosωt
a=-a0sinωt

Question 17

Write x0, v0 and a0 in terms of r and ω where r is the radius of the circle.

Answer 17

x0=r
V0 = ωr
a0 = ω^2r

Question 18

Express v in terms of x.

Answer 18

v=+_ ω(x0^2-x^2)^1/2

Question 19

When x= 0, v is _____. Vice versa.

Answer 19

Maximum.

Question 20

What are the conditions for a pendulum to be in SHM?

Answer 20

θ is very small so Sinθ is approximately equal to θ which is approximately equal to x/l where l is the length of the string. F on mass = -mgsinθ = -mgx/l.
ω^2 = g/T T= 2π/ω = 2π(l/g)^1/2

Question 21

What is the Ek equation for a body undergoing SHM?

Answer 21

Ek = 1/2 mv^2 = 1/2mω^2(x0^2- x^2)

Question 22

What is the equation for potential energy for SHM?

Answer 22

In a pendulum, Ep= 0.5mω^2x^2. (Why?)

Question 23

In an energy time graph, what is the relationship between Ep and Ek?

Answer 23

And TE = Ep + Ek, the graph of Ek is one that an overturned Ep graph.

Question 24

What is light damping?

Answer 24

It causes a displaces system to oscillate with gradual decreasing amplitude.

Question 25

What is critical damping?

Answer 25

It causes a displaced system to return to rest at is equilibrium position in the shortest time possible without oscillating.

Question 26

What is heavy damping?

Answer 26

It causes the displaced system to take a Long time to return to its equilibrium position without oscillating.

Question 27

What are forced oscillations?

Answer 27

It is when an external periodic force, the oscillating force (at driving frequency) is applied to sustain oscillations, doing work against the dissipating forces (or to replace the energy post to dissipating forced.

Question 28

What is natural frequency?

Answer 28

It is the frequency when a system oscillates without any external force.

Question 29

Amplitude is at maximum when driving frequency is _____.

Answer 29

Equal to natural frequency.

Question 30

For a resonance curve, degree if damping affects: the greater the damping the lower the _____.

Answer 30

Height and shape of the curve. Natural frequency and maximum amplitude the driving oscillation can provide.

Question 31

Why is it that when the driving frequency is equal to the natural frequency, the amplitude is the highest?

Answer 31

Energy is most easily transferred as the driving force F is always reinforcing the restoring force of the forced oscillations ie they are in the same direction.

Question 32

What are the lags depending on the frequency of the forced oscillations?

Answer 32

f0: -π

Question 33

What is steady state?

Answer 33

It is when after a period of time of forced oscillations the system settles down to a state with steady amplitude a phase difference. The amplitude and phase difference is determined by the position of the driving frequency compared to the natural frequency.

Question 34

What is resonance?

Answer 34

It is when driving frequency = natural frequency.

Question 35

How can resonance cause problems for structures if not damped internally?

Answer 35

Oscillation occurs and if resonance frequency is reached it will cause the object to break.

Question 36

What are the ways to reduce destruction by resonance?

Answer 36

• Increasing damping in the structure

- change shape, size, mass and mass distribution to change natural frequencies or frequency of driving oscillations.