University:
University of Cambridge
Course:
0625 IGCSE | Physics
Academic year:

2023
Views:

256

Pages:

2
Author:

Deddy A.

Vibrations Chapter 13 & Waves 13.1 Hooke's Law F= kx Spring spring force constant displacement from equil. position (N/m) a= K m from ma F=-kx Simple harmonic motion: the net force exerted by a spring is proportional to ex from the equil point & is always directed toward the equil point. •F is not constant a is not constant E is constant 13.2 Elastic PE PE=Kx2 when x reaches V=0, other max. A, V=0, wise it'd be moving KEO, b/c ie depends on a= max, and E=KA2 a = max, b/c F is at a max & they're proportional (F) when x=0,7 reaches its max. value and EmVmax (KE-PE, PE) = (KE PEPE) law of conservation of energy (spring + gravitational force) neglects friction V=(A2-x²) →(-) moving left. speed of object as a function of x →(+): moving right When x is positive (the spring is stretched), the spring force is to the left. When is zero (the spring is unstretched). the spring force is zero. F-0 When x is negative (the spring is compressed), the spring force is to the right. F 0 W (KE-PEg+PE) - (KEPE,PE). ↓ work done by non-conservative = A mechanical E forces ↓ friction present Initially, the methunhaler Here the metal energy is the em of the back's kneenerg and the elastic potential energy smoted as the comprend ping When the luck comes is test, the mechanical energy extired Figure 13.1 The force exerted by a spring on an object varies with the displacement of the object from the equilibrium position, -0. total E When the taock leaves the spring the awchanical ensti Describing oscillations Amplitude: A Maximum distance, Xmax, from equilibrium position. Period: T Time taken for one oscillation. Frequency: f Number of oscillations per second. f= 1 Frequency has units of s¹ or Hertz (Hz), where 1 Hz = 1s1. Angular frequency: w Number of radians per second. w = 2πξ m Angular frequency has units of rad/s. Simple Pendulum. The restoring force causing the pendulum to oscillate harmonically is the tangential component of the gravity force-mgsin 8. F=-mgsine = A simple pendulum undergoes Simple Harmonic Motion (SHM). Period of pendulum oscillations T = 2π L 9 Frequency of pendulum oscillations f= 1 9 2π L L T W period of block-spring Oscillations. T=2 freq. of b-s oscillations: m Angular frequency of pendulum oscillations mg sin mg cos mg Figure 13.15 A simple pendulum consists of a bob of mass suspended by a light string of length I. (L is the distance from the pivot to the center of mass of the bob.) VI 3