Simple Harmonic Motion (Edexcel A-Level Further Mathematics): Quizzes

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Simple Harmonic Motion
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In SHM, acceleration is proportional to what quantity?

Distance from center of motion

What is the defining equation for simple harmonic motion?

d2xdt2=ω2x\frac{d^2x}{dt^2} = -\omega^2 x

In circular motion, where is acceleration always directed?

Toward the center of the circle

What is the characteristic equation for x¨=ω2x\ddot{x} = -\omega^2 x?

m2+ω2=0m^2 + \omega^2 = 0

What are the roots of the characteristic equation m2+ω2=0m^2 + \omega^2 = 0?

m=±iωm = \pm i\omega

What is the general solution to x¨=ω2x\ddot{x} = -\omega^2 x?

x=Asin(ωt)+Bcos(ωt)x = A\sin(\omega t) + B\cos(\omega t)

What alternative form can the general solution be transformed to?

x=Rsin(ωt+α)x = R\sin(\omega t + \alpha)

What is the constant of proportionality in the SHM equation?

ω2-\omega^2

What does a dot above a variable indicate?

Differentiation with respect to time

By what angle is circular motion rotated to view it as pendulum-like motion?

90 degrees

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