Chp 8: Oscillations

Question 1

Define Simple Harmonic Motion:

Answer 1

It is the motion of a particle about a fixed point such that its acceleration is directly proportional to its displacement from the equilibrium point and the direction of the acceleration is always in the opposite directions of the particle’s displacement.

Question 2

Define Angular Frequency:

Answer 2

It is the rate of change of phase angle of the oscillation.

Question 3

Define Amplitude:

Answer 3

Amplitude is the magnitude of the maximum displacement of a particle from its equilibrium position.

Question 4

Define Period:

Answer 4

Period is the time taken for one complete oscillation

Question 5

Define Frequency:

Answer 5

Frequency is the number of oscillations per unit time.

Question 6

Define Free Oscillations:

Answer 6

object oscillates with no resistive and driving force acting on it.

Its total energy and amplitude remain constant with time.

Question 7

Define Damped Oscillations:

Answer 7

total energy of oscillations decreases due to the presence of dissipative forces like drag.

Question 8

Define Light Damping:

Answer 8

amplitude decays exponentially with time.

frequency of oscillations is slightly smaller than the undamped frequency.

Question 9

Define Critical Damping:

Answer 9

no oscillation
system returns to the equilibrium
position in the shortest time

Question 10

Define Heavy Damping:

Answer 10

no oscillation

system takes a long time to return to its equilibrium position

Question 11

Define Forced Oscillations:

Answer 11

external periodic driving force is supplied to the
oscillating system

Question 12

Define Resonance:

Answer 12

driving frequency matches the natural frequency of the oscillating system

system responds at a maximum amplitude of oscillation.

At resonance there is max transfer of energy from the driver to the oscillating system.

Question 13

State the acceleration of the plate at which the sand first loses contact with the plate.
Explain your reasoning.

Answer 13

When the plate is accelerating downward at 9.81 ms-2 , the sand will be undergoing acceleration of free fall. At this acceleration, the gravitational force acting on the sand particle is just sufficient to cause the acceleration of the sand particle and thus normal contact force equals zero.

Question 14

describe the restoring force that gives rise to the oscillations OF BLOCK ON WATER

Answer 14

At equilibrium position, the upthrust equals to weight. As the block is displaced downwards from its equilibrium position, the volume of water displaced increases and hence, upthrust increases. The restoring force for the floating block is the resultant force due to the upthrust on the block by the water and the block’s weight.

Question 15

describe the restoring force that gives rise to the oscillations OF THE BOBBBBBBBBBBBBBBBBBB

Answer 15

At the equilibrium position, the upward tension force is equal to the downward
weight. When the pendulum is displace leftwards along a circular arc, the
component of the weight tangent to the arc acts towards the right and is parallel to its displacement. This component provides the restoring force.

Question 16

Should the timing recorded of the period of oscillation of a SHM be at a position where the displacement is zero or the displacement is maximum?

Answer 16

Since object tends to stay at the position of maximum displacement for a longer period of time, harder to know exact instant to stop the stopwatch.

So, more uncertainty in measuring a time interval for a number of oscillations to occur.

So, timing should record when displacement is zero.

Question 17

Showing SHM (eg. 𝒂 = −(𝒌/𝒎)𝒙):

Answer 17

1. k/m constant means a ∝ x
2. -ve sign means a always opp direction of x, hence…

Question 18

two features of the graph which suggests that particle P is moving in simple harmonic motion (a-w graph)

Answer 18

1. straight line thru origin -> a ∝ x
2. -ve gradient shows a always opp direction to its displacement

Question 19

In normal use, the loudspeaker produces a range of frequencies of sound. Suggest why it is important that the natural frequencies of vibration of the cone of the loudspeaker is not within this range of frequencies.

Answer 19

• Vibration of the cone is driven by the electrical signal.
• If frequency of the sound produced matches the natural frequency of the cone, resonance occurs,so cone vibrates at maximum amplitude.

-Since e loudspeaker produces a range of frequencies of sound, sound is distorted (louder for sound of frequencies near the natural frequency of the cone)

Question 20

Why a lightly damped oscillating system experiences a progressive decrease in its amplitude?

Answer 20

• system loses energy due to WDagainst dissipative forces cuz it leads to the thermal energy produced.
• since energy of the system ∝ amplitude² , amplitude is progressively reduced.

Question 21

A spring is assumed to be light. In practice, the spring will have some mass. Assuming that the spring constant k is unchanged, suggest and explain the effect on the frequency of oscillation of having a spring with mass.

Answer 21

• If spring got mass, effective mass of the mass-spring oscillator will increase.
• since 𝑇 = 2𝜋 √( 𝑚/𝑘) ) and f=1/T, frequency of oscillation will decrease.