Simple Harmonic Motion

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Presentation transcript:

Simple Harmonic Motion Oscillatory Motion

https://www.youtube.com/watch?v=yVkdfJ9PkRQ&t=9s

Period and Frequency Period: Time needed to complete one cycle Frequency: Number of cycles per second

Two Types Mass and Spring Pendulum

Hooke’s Law (Restoring Force) Where k is the force or spring constant The negative sign indicates the direction of the force is always pointing toward the equilibrium position, so it is referred to as a restoring force. In SHM the restoring force is proportional to the displacement.

Circular Motion vs. SHM

ω?

Copyright (c) 1998-2005 "Siltec ltd" Pend-avi Copyright (c) 1998-2005 "Siltec ltd"

SHM Equation where A is the amplitude

Cosine vs. Sine Graphs

Energy of a Mass and Spring

Acceleration of Mass and Spring

Mass and Spring x = 0 v = ±Aω a = 0 K = ½ kA2 Us = 0 x = A v = 0 a = -kA/m K = 0 Us = ½ kA2 x = -A v = 0 a = kA/m K = 0 Us = ½ kA2

Pendulum q L Lcosθ Dy

Pendulum Restoring Force The restoring force is proportional to sinq, not q. This means the simple pendulum is not true SHM, but for small angles it can be modeled as SHM.

q v = 0 K = 0 Ug = mgDy v = 0 K = 0 Ug = mgDy v = ± vmax K = mgDy Ug = 0

m = 0.2 kg k = 20 N/m Block is pulled 12 cm to the right and released. What is the equation x(t)? What is the block’s displacement at 2.4 s? What is E for the system? What is the max. speed the block reaches? What is the block’s speed 2 cm to the right of the equilibrium position?

What is the equation x(t)?

What is the block’s displacement at 2.4 s?

What is E for the system?

What is the max. speed the block reaches?

What is the block’s speed 2 cm to the right of the equilibrium position?

A pendulum has a length of 2. 0 m A pendulum has a length of 2.0 m. It is displaced 20 degrees from the vertical and released. The mass of the bob is 1.0 kg. Determine the following: q L What is the period? What is the frequency? What is E? What is the maximum speed of the pendulum bob?

What is the period?

What is the frequency?

What is E? At maximum displacement, K=0 and U=mgDy

What is the maximum speed of the pendulum bob?