c) Graphs

g) graphical methods to relate the changes in displacement, velocity, and acceleration during simple harmonic motion

d) solutions to the equation a = -ω²x e.g. x = Acosωt or x = Asinωt

e) velocity v = ±ω√(A² - x²) hence v_max = ωA

graph of displacement against time for an object in simple harmonic motion

starting at the positive amplitude

x = Acos(ωt)

• displacement (m) = amplitude (m) x cos(angular frequency (rads^-1) x time (s))

graph of displacement against time for an object in simple harmonic motion

starting at the equilibrium position

x = Asin(ωt)

• displacement (m) = amplitude (m) × sin(angular frequency (rads^-1) × time (s))

graph of velocity against time for an object in simple harmonic motion

v = ±ω√(A² - x²)

• velocity (ms^-1) = ±angular frequency × √(amplitude² - displacement²)

v_max = ωA

• velocity at equilibrium position (ms^-1) = angular frequency (rads^-1) × amplitude (m)

graph of acceleration against time for an object in simple harmonic motion