Lecture27

# Lecture27 - Summary Simple Harmonic Motion TYPICAL EQUATION...

This preview shows pages 1–4. Sign up to view the full content.

Summary Simple Harmonic Motion d 2 x + c x =0 dt 2 TYPICAL EQUATION for SHM Solution x(t) = A cos ( ω t + ϕ ) ω = c Τ = 2 π / ω x (t=0) = x 0 v (t=0) = v 0 a (t=0) = a 0 Initial Condition – to determine A, ϕ t x A T ϕ Velocity and acceleration Note : v and a always opposite to x a(t) = - A ω 2 cos ( ω t + ϕ ) v(t) = - A ω sin ( ω t + ϕ ) = + ω A 2 – x 2 Being x(0) = A cos ϕ = x 0 ϕ = arccos (x 0 /A)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example L eq L 1 m 2 m 1 System in equilibrium. Break the spring and m 1 starts to oscillate. Find x(t) for m 1 . Neglect friction
“Vertical” spring as a simple harmonic oscillator New equilibrium position Oscillation around new position Σ F = - ky + mg - ky + mg = 0 (at equilib.) From Newton’s second law: d 2 y dt 2 = - k m + g 1 st step : Reduce it to simple differential equation 1) Add gravity to equation of motion Only change is in the equilibrium position! y

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 11

Lecture27 - Summary Simple Harmonic Motion TYPICAL EQUATION...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online