1.2 Simple Harmonic Motion (SHM) (unfinished)

Given this image, what is A?

amplitude or the maximum distance from the equilibrium position to either endpoint of the motion

In relation to Simple Harmonic Motion, what is x(t)? What is it equal to?

x(t) is the displacement of the object

x(t) = Acos(ωt)

In relation to Simple Harmonic Motion, what is t?

t is time

In relation to Simple Harmonic Motion, what is ω? What are its units?

angular frequency in (rad/s)

In relation to Simple Harmonic Motion, what is f? What are its units?

# of times a cycle (back + forth) is completed in a second

units: 1/s = s⁻¹ = Hz

ω=? Why does it equal that?

2πf

angular frequency (ω) measures how many radians are covered each second; one full cycle equals 2π radians, so ω = (2π times) /(cycles per second) = 2πƒ

In relation to Simple Harmonic Motion, what is T? What are its units? What is it equal to?

period = how long it takes (s) to complete 1 cycle

units: s

What is the relationship between T and f?

T = \frac{1}{f}

Relate time to angular frequency

\omega t=\theta

What is the arrow pointing too?

when cos(ωt) = 0

when cos(ωt) = 0, what is time (t) equal to? Then relate it to frequency.

1. \cos\left(\omega t\right)=0

2. \omega t=\frac{\pi}{2}

3. t=\frac{\pi}{2\omega}

∵\omega=2\pi f

∴t=\frac{\pi}{2\cdot2\pi f} {pi cancels out}

∴t=\frac{1}{4f}