Simple Harmonic Motion

Question 1

What is simple Harmonic Motion?

Answer 1

An oscillatory motion in which acceleration is directly proportional to displace men and is always directed towards the equilibrium position

A = -constant x displacement (x)

Question 2

What is the equation for acceleration in Simple Harmonic Motion?

Answer 2

A = -v^2/r = -w^2r

Question 3

Describe the acceleration of a body in SHM

Answer 3

The body is always accelerating towards the Centre of the Motion except at the center of the Motion where the acceleration is zero.
Think of a pendulum where the acceleration is at its max acceleration at the end but zero. In the middle as that is the equilibrium position.

Question 4

Describe why a body in SHM keeps swinging past the equilibrium position

Answer 4

A restoring force tries to return the system to equilibrium

The system has inertia and overshoots the equilibrium position

Question 5

What is the mathematical expression for displacement in SHM?

Answer 5

A = -w^2x where w = 2(pi)f

Therefore

Displacement x = acos (wt)

And x = asin (wt)

Question 6

What is the equation for hookes law?

Answer 6

F = kx or -kx if force is the restoring force

Question 7

How is time period calculated in a mass-spring system?

Answer 7

T = 2(pi) root m/k

Gotten by combining hookes law with acceleration in circular motion

Question 8

Why does an object oscillate with SHM? What is the equation for time period in a pendulum?

Answer 8

Acceleration is proportional to the displacement from equilibrium and always acts towards it.

T = 2(Pi) root L/g

Question 9

What is the speed equation in SHM

Answer 9

V = +/- w root A^2 - x^2

Question 10

How is energy calculated in SHM?

Answer 10

Ep = 1/2kx^2

ET = 1/2kA^2

ET = Ek + Ep

Ek = 1/2k(A^2 - x^2)

Question 11

What is the curve in an energy displacement graph in SHM

Answer 11

Potential energy is a parabolic curve

Kinetic energy is an inverted parabola

The sum of Ek and Ep is always 1/w kA^2

Question 12

What is damping in oscillation

Answer 12

The dissipation of energy over time

Question 13

What are the types of damping?

Answer 13

Light, critical and heavy

Question 14

Describe light, critical and heavy damping

Answer 14

1. Light damping: Defined oscillations are observed, but the amplitude of oscillation is reduced gradually with time. The oscillation of a child on a swing without periodic push will loose its energy gradually and be lightly damped.
2. Critical Damping: The system returns to its equilibrium position in the shortest possible time without any oscillation. Critical Damping is important so as to prevent a large number of oscillations and there being too long a time when the system cannot respond to further disturbances. Instruments such as balances and electrical meters are critically damped so that the pointer moves quickly to the correct position without oscillating.
3. Heavy Damping: The system returns to the equilibrium position very slowly, without any oscillation. Heavy damping occurs when the resistive forces exceed those of critical damping. A push tap in a public toilet is an example of Heavy Damping.

Question 15

What happens when the applied frequency becomes larger than the resonant frequency of the mass-spring system?

Answer 15

• the amplitude of oscillations decreases more and more,
• the phase difference between the displacement and the periodic force increases from 𝜋/2 until the displacement is 𝜋 radians out of phase with the periodic force.

Question 16

What happens when there is little or no damping at resonance in an oscillating system?

Answer 16

For an oscillating system with little or no damping, at resonance,
the applied frequency of the periodic force = the natural frequency of the system

Question 17

What happens when the system is oscillating at maximum amplitude?

Answer 17

When the system is oscillating at the maximum amplitude, the phase difference between the displacement and the periodic force 𝜋/2

The periodic force is then exactly in phase with the velocity of the oscillating system, and the system is in resonance. The frequency at the maximum amplitude is called the resonant frequency.