Simple Harmonic Motion

Question 1

Give:

characteristics of oscillatory motion

Answer 1

periodic
repetitive
circular
to and fro
back and forth

Question 2

Define:

Period (T) of an oscillation

Answer 2

time taken to make 1 complete cycle of the motion

Question 3

Define:

Frequency (f) of an oscillation

Answer 3

number of cycles made per second

Question 4

Define:

SHM

Answer 4

specific type of oscillatory motion where

the acceleration of the oscillating mass must be proportional to the displacement of the mass from the equilibrium position

The direction of the acceleration opposes the displacement

a ∝ - y

Question 5

What type of force causes SHM?

What direction is this force?

Answer 5

Restoring force

Towards the equilibrium position

Question 6

Give:

Equation for acceleration and displacement

Answer 6

a = y ω^2

Question 7

Give:

Name for ω in SHM

Answer 7

Angular frequency

ω = 2πf = 2π / T = θ / t

Question 8

Give:

equation for SHM displacement

Answer 8

y = A sin ωt

Question 9

Give:

equation for SHM velocity

Answer 9

dy/dt = Aω cos ωt = v

Question 10

Give:

equation for SHM acceleration

Answer 10

dv/dt = -A ω^2 sin ωt = a

a = - y ω^2

Question 11

Give:

Equation for restoring force on a spring

Answer 11

F = -k y

Question 12

Derive the equation:

T = 2π√ (m/k)

or

f = 1/2π √ (k/m)

Mass on a Spring

Answer 12

a = F/m

–> a = -k y / m

–> -y ω^2 = (-k y) / m

–> ω^2 = k / m

–> ω = √ (k/m)

–> T = 2π / ω

–> T = 2π / √ (k/m)

–> T = 2π√ (m/k)