Chapter 18 - Simple harmonic motion

Question 1

What is the equation for the phase difference of two objects undergoing simple harmonic motion?

Answer 1

T

where Δt is the constant time gap between two oscillating objects

Question 2

What is simple harmonic motion?

Answer 2

Oscillating motion in which:
• acceleration is always in the opposite direction to the displacement
• a ∝ -x 2
with constant of proportionality ω
(An oscillating object speeds up as it returns to its equilibrium position and slows down as it moves away from the equilibrium).

Question 3

What is the relationship between the period and frequency of an oscillation and the amplitude in SHM?

Answer 3

There is none.
In SHM, the frequency and period of an oscillation are independent of the amplitude (i.e. constant for a given oscillation).

Question 4

In SHM, we use the magnitude of angular velocity, ω, which is defined as…

Answer 4

…angular frequency.

Question 5

What is the restoring force?

Answer 5

A force which acts to bring a body to its equilibrium position.
This force is present in SHM.
The restoring force depends on the system.

Question 6

What factors affect the period of an oscillation of a mass-spring system?

Hint: It is shown by the equation

Answer 6

• Mass (m↑, T↑)

- Stiffness (Spring constant) (k↑, T↓ )

Question 7

What factors affect the period of an oscillation of a simple pendulum?

Hint: It is shown by the equation

Answer 7

• Length of rod/string (L↑,T↑)

- g (g↑, T↓)

Question 8

What is the equation for the kinetic energy of a simple harmonic oscillator?

Answer 8

1 2 2
Ek = —k(A - x )
2

Question 9

What is the equation for the velocity and speed of an object undergoing SHM?
What is the equation for the maximum speed of an object undergoing SHM?

Answer 9

v = ±ωx
v = velocity

v = ωx
v= speed

vmax = ωA

Question 10

What is the equation for the acceleration of an object undergoing SHM?
What is the equation for the maximum acceleration of an object undergoing SHM?

Answer 10

2
a = 𝜔 x
2
amax = 𝜔 A

Question 11

What is free oscillation?

Answer 11

Oscillation of an object caused by a restoring force with no external forces (therefore, constant amplitude, constant total energy).
An object oscillating at its natural frequency.

Question 12

What is natural frequency?

Answer 12

The frequency that a system oscillates without the presence of external forces.
(The frequency of free oscillations of an oscillating system).

Question 13

What is a periodic force?

Answer 13

A force that varies regularly in magnitude with a definite time period.
A force applied at regular intervals.

Question 14

What is a forced oscillation?

Answer 14

The oscillation of an object subjected to an external periodic force.

Question 15

What is driving/applied frequency?

Answer 15

The frequency of a periodic force.

Question 16

An object undergoing forced oscillation oscillates at the _______ frequency of the _______ force rather than its ______ frequency.

Answer 16

An object undergoing forced oscillation oscillates at the driving/applied frequency of the periodic force rather than its natural frequency.

Question 17

What is damping?

Answer 17

Any effect that tends to reduce the amplitude of oscillations (e.g. friction).

Question 18

What is a damped oscillation?

Answer 18

One where the amplitude of the oscillations decrease over time as a result of resistive forces.

Question 19

What is light damping?

Answer 19

Damping in which the resistive forces acting on an oscillating mass are small. The amplitude decreases over a period of time during oscillation.

Question 20

What is critical damping?

Answer 20

When the displacement of an object decreases to zero in the shortest time possible without any oscillation.

Question 21

What is heavy damping?

Answer 21

When the system returns to the equilibrium position very slowly without any oscillation.

Question 22

What is resonance?

Answer 22

The condition in which an object or system is subjected to an oscillating force having a frequency (driving frequency) equal to its natural frequency. This causes increasing amplitude of oscillation up to the resonant frequency.

Question 23

What is resonant frequency?

Answer 23

The frequency of oscillation at which the energy supplied by an external driving force is equal to the energy lost per cycle (to resistive forces). The amplitude stops increasing. The amplitude has reached a maximum.

Question 24

How do the Barton’s Pendulums show resonance?

Answer 24

The small pendulum with the same length string as the heavy ‘driver’ pendulum oscillates at the same frequency as the driving frequency (frequency of driver pendulum)