SHM

Question 1

what is the equation for acceleration, using: ω and x?
SHM

Answer 1

a = -(ω^2)x

(-) because a is proportional to displacement in opposite direction

Question 2

what is the equation for displacement, using: A, ω and t?
SHM

Answer 2

x = Acos(ωt)

where:
• x = displacement from equilibrium
• A = maximum displacement from equilibrium [or amplitude]
• ω = angular velocity
• t = time

cos when pendulum starts at A, sin when pendulum starts at 0 [or equilibrium]

Question 3

what is the equation for linear speed, using: ω, A and x?
SHM

Answer 3

v = ±ω√(A^2 - x^2)

where:
• ω = angular velocity
• A = amplitude
• x = displacement from midpoint or equilibrium

Question 4

what is the maximum linear speed, using: ω and A?
SHM

Answer 4

vmax = ωA

where:
• ω = angular velocity
• A = amplitude

equation is for when pendulum is at midpoint [or equilibrium]

bc when when pendulum passes through midpoint [or equilibrium] (so x = 0), KE = max and PE = 0, so v = ±ω√(A^2 - x^2) => v = ±ω√(A^2 - (0)^2) => v = ±ωA => v = ωA

Question 5

what is maximum acceleration, using: ω and A?
SHM

Answer 5

a = (ω^2)A

equation is for when pendulum is at amplitude

Question 6

what is the equation for time period, using: L and g?
SHM

Answer 6

T = 2π√(L / g)

where:
• T = time period
• L = length of string
• g = gravitational field strength

there is no m in this equation so T would be the same no matter what mass the pendulum has

Question 7

what is the mass of the spring, using: T and k?
SHM

Answer 7

T = 2π√(m / k)

where:
• T = time period
• k = spring constant

there is no g in this equation so T would be the same no matter in what gravitational field you do it, eg) moon, mars, earth, etc